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Annexure-I

1 Integrated M.SC. Statistics syllabus

COURSE STRUCTURE OF INT. M. SC. STATISTICS

Integrated M. Sc. I to VI Semester Sem. Paper Code Title Credit

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I BST 101 Analysis of Univariate Data & Elements of Probability 4 3 1 0 BST 102 Practical based on BST 101 1 0 0 2

II BST 103 Analysis of Bivariate Data & Random Variables 4 3 1 0 BST 104 Practical based on BST 103 1 0 0 1

III BST 201 Probability Distributions –I 4 3 1 0 BST 202 Practicals based on BST 201 1 0 0 1

IV BST 203 Statistical Inference –I 4 3 1 0 BST 204 Practicals based on BST 203 1 0 0 1

V

BST 301 Probability Distributions -II 4 3 1 0 BST 302 Sample Survey 4 3 1 0 BST 303 Time Series & Index Numbers 4 3 1 0 BST 304 Statistical Inference –II 4 3 1 0 BST 305 Numerical Analysis 4 3 1 0 BST 306 Practicals 4 0 0 4

VI

BST 351 Elements of Reliability & Survival Analysis 4 3 1 0 BST 352 Design of Experiments-I 4 3 1 0 BST 353 Statistical Process Control & Vital Statistics 4 3 1 0 BST 354 Operation Research 4 3 1 0 BST 355 Official Statistics & Demand Analysis 4 3 1 0 BST 356 Practicals 4 0 0 4

Integrated M. Sc. VII Semester

Paper Code Title Credit Credit MST 101 Probability Theory 4 3 1 0 MST 102 Distribution Theory 4 3 1 0 MST 103 Linear Algebra and Matrix Theory 4 3 1 0 MST 104 Sampling Theory 4 3 1 0 MST 105 R: Statistical Programming Language 4 3 1 0 MST 106 Practicals 4 0 0 4

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Integrated M. Sc. VIII Semester

Paper Code Title Credit Credit MST 201 Estimation and Testing of Hypotheses 4 3 1 MST 202 Linear Models 4 3 1 MST 203 Stochastic Models 4 3 1 MST 206 Practicals 4 0 0

Elective Courses

Paper Code Title Pre-requisite

Credit Credit

MST 221 Design of experiment –II 4 3 1 MST 222 Econometrics 4 3 1 MST 223 Financial Mathematics 4 3 1 MST 224 Economics for Actuarial Science 4 3 1 MST 225 Machine Learning 4 3 1 MST 226 Modeling and Simulation (Mathematics, MTM 204) 4 3 1

MST 227 Mathematical Software and Tools (Mathematics, MTM 206) 4 3 1

Integrated M. Sc. IX Semester

Paper Code Title Pre-requisite Credit Credit MST 301 Decision Theory and Non Parametric Inference 4 3 1 0 MST 302 Time Series Analysis and Forecasting MST 303 Multivariate Analysis 4 3 1 0 MST 306 Practicals 4 0 0 4

Elective Courses

Paper Code Title Pre-requisite Credit Credit MST 321 Statistical Quality Control 4 3 1 0 MST 322 Stochastic Finance 4 3 1 0 MST 323 Contingencies 4 3 1 0 MST 324 Principle and Practices of Insurance 4 3 1 0 MST 325 Data Mining 4 3 1 0

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Integrated M. Sc. X Semester

Paper Code Title Pre-requisite Credit Credit MST 401 National Development Statistics 4 3 1 0 MST 406 Practicals 4 0 0 4 MST 410 Project 8 - - -

Elective Courses Paper Code Title Pre-requisite Credit Credit MST 421 Survival Models and Analysis 4 3 1 0 MST 422 Advanced Bayesian Inference 4 3 1 0 MST 423 Statistical Quality Management 4 3 1 0 MST 424 Statistical Methods for Non-life Insurance 4 3 1 0 MST 425 Life and Health Insurance 4 3 1 0 MST 426 Employee Benefit Plans 4 3 1 0 MST 427 Valuation and Loss Reserving 4 3 1 0 MST 428 Finance and Financial Reporting 4 3 1 0

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PAPER CODE BST 101 PAPER NAME Analysis of Univariate Data & Elements of Probability CREDIT 04(3-1-0) TOTAL HOURS 43 Unit-1 Lectures: 15 Meaning and scope of the word ‘Statistics’. Data types: Qualitative and Quantitative Data scales of measurements: nominal, ordinal, ratio, interval Representation: Tabulation Compilation, Classification. Graphical and diagrammatic representation: Bar diagrams, multiple and stack bar diagrams, Histogram, Frequency Polygon, Frequency Curve, Ogive, Pie diagram, Box plot, Stem and leaf diagrams.

Measures of Central Tendency: Concept, requirements of a good measure. Arithmetic Mean (A.M), Geometric Mean (G.M), Harmonic Mean (H.M.), Median, Mode: properties, merits and demerits. Quartiles, Deciles and Percentiles, Graphical method of determination of Median, Mode and Quantiles.

Unit-2 Lectures: 08 Measures of Dispersion: Concept, Requirements of a good measure of dispersion. Range: Quartile Deviation (Semi-interquartile range): Coefficient of Q.D. Mean Deviation (M. D.), Proof of Minimal property of M.D. Mean Square Deviation (M.S.D.): proof of Minimal property of M.S.D. Variance and Standard Deviation (S.D): Effect of change of origin and scale, S.D. of pooled data (proof for two roups), Coefficient of Variation (CV).

Moments: Raw moments and Central moments, relation between central moments and raw moments, Sheppard correction for moments (without derivation), Skewness: Measure of skewness, Types of skewness, Kurtosis, Types of kurtosis, Measure of kurtosis. Unit-3 Lectures: 10 Concepts of experiments: deterministic, probabilistic, outcomes of experiments. Sample space, Discrete (finite and countably infinite) and continuous sample space, Event, Elementary event, Compound event. Algebra of events (Union, Intersection, Complementation), De Morgan’s law. Definitions of Mutually exclusive events, Exhaustive events, Venn diagram.

Definition; Axiomatic definition of probability; Addition theorem (Proof of the result up to three events), Elementary properties, Classical definition of Probability as a special case, Probability as an approximation to the relative frequency, illustrative examples for computation of events based on Permutations and Combinations, with and without replacements, impossible events, certain events.

Unit-4 Lectures: 10 Definition of conditional probability of an event, Multiplication theorem for two events, Independence of events: Pairwise and Mutual Independence of events. Partition of sample space. Statement and proof of Bayes’ theorem. References

1. Rohatgi V. K. and Saleh A. K. Md. E., An Introduction to probability and Statistics. John Wiley & Sons (Asia).

2. Mukhopadhyay, P., Mathematical Statistics, new Central Book Agency Pvt. Ltd., Calcutta.

3. Hoel P. G., Introduction to Mathematical Statistics, Asia Publishing House. 4. Meyer P. L., Introductory Probability and Statistical Applications, Addision Wesley. 5. AM Goon, M K Gupta and B. Das Gupta, Fundamentals of Statistics, Volume-I, World Press.

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PAPER CODE BST 102 PAPER NAME Practical based on BST 101 CREDIT 01 (0-0-1) TOTAL HOURS 45 CONTENT Students will be required to do parcticals, based on topics listed below, using MS Excel:

1. Introduction to MS Excel: Data storage, elementary calculations and graphical representations. 2. Actual conduct of experiments and comparing relative frequencies with actual probabilities. 3. Computation of conditional probabilities (Bayes’ theorem) 4. Tabulation and Construction of frequency distribution 5. Diagrammatic (Multiple stack bar diagrams, histogram, stem and leaf, pie chart) and graphical

(frequency polygon, frequency curve) presentation of the frequency distribution. 6. Measures of Central tendency – I (ungrouped data). 7. Measures of Central tendency – II (grouped data). 8. Measures of Central tendency – III (pooled data). 9. Computation of quantiles by use of Ogive curves, 10. Measures of the Dispersion – I (ungrouped data). 11. Measures of the Dispersion – II (grouped data). 12. Moments, Skewness & Kurtosis-I (ungrouped data). 13. Moments, Skewness & Kurtosis-II (grouped data). 14. Computation of raw, central moments, Pearson’s coefficient of skewness and kurtosis.

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PAPER CODE BST 103 PAPER NAME Analysis of Bivariate Data & Random Variables CREDIT 04(3-1-0) TOTAL HOURS 44 Unit-2 Lectures: 8 Bivariate Data. Scatter diagram. The concept of dependency, illustrative real life examples. Covariance: Definition, Effect of change of origin and scale. Karl Pearson’s coefficient of correlation (r): Definition, Properties, Spearman’s rank correlation coefficient: Definition, Interpretation when r = -1, 0, 1, Derivation of the formula for without ties and Modification of the formula for with-ties Computation, variance of linear combination of variables. Unit-2 Lectures: 8 Concept of regression, Lines of regression, Fitting of lines of regression by the least square method. Regression coefficients (bxy, byx) and their geometric interpretations, Properties. Derivation of the point of intersection of two regression lines and the acute angle between the two lines of regression. Unit-3 Lectures: 14 Definition of random variable, Discrete and continuous and mixed type of random variables, Definition of distribution function, Distributions function (df) of random variable, Probability distribution of function of random variable. Probability mass function (p.m.f.) and cumulative distribution function (c.d.f.) of a discrete random variable, Probability density function (p.d.f.) and cumulative distribution function (c.d.f.) of a continuous random variable, relation between df and pmf/pdf, Median and Mode of a univariate discrete and continuous random variables. Unit-4 Lectures: 14 Definition of expectation of a random variable, expectation of a function of a random variable, simple properties, Definitions of mean, variance of univariate distributions, Effect of change of origin and scale on mean and variance, Definition of raw, central moments, mean deviation. Pearson’s coefficient of skewness, kurtosis, Definitions probability generating function (p.g.f.), moment generating function (m.g.f.)and characteristic function of a random variable, Effects of change of origin and scale. p.g.f. of sum of two independent random variables is the product of p.g.f.s (statement only), Derivation of mean and variance by using p.g.f. References

1. Mood A. M. , Grabyll R. A. and Boes D. C., Introduction to the theory of Statistics, Tata MeGraw Hill

2. Mukhopadhyay, P., Mathematical Statistics, new Central Book Agency Pvt. Ltd., Calcutta. 3. AM Goon, M K Gupta and B. Das Gupta, Fundamentals of Statistics, Volume-I, World Press. 4. Ross Sheldon M., Introduction to Probability Models, Academic Press 5. Rao, B. L. S. Prakash, A first course in probability and Statistics, World Scientific.

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PAPER CODE BST 104 PAPER NAME Practical based on BST 103 CREDIT 01 (0-0-1) TOTAL HOURS 45 CONTENTS Students will be required to do practicals, based on topics listed below, using MS Excel:

1. Advanced level commands /programming using MSEXCEL 2. Scatter diagram for bivariate data and interoperation. 3. Correlation coefficient: grouped data. 4. Correlation coefficient: ungrouped data 5. Spearman’s Rank correlation: ungrouped data. 6. Regression-I (ungrouped data). 7. Regression-II (grouped data).

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PAPER CODE BST 201 PAPER NAME Probability Distributions –I CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 8 General concept of a finite discrete random variable, computation of their means and variances, Concept of discrete probability distributions. Uniform, Bernoulli, Binomial, Poisson and geometric distributions with their properties and applications. Unit-2 Lectures: 8 Definition of continuous random variable (r.v.), illustrations, probability density function (p.d.f.), and cumulative distribution function (c.d.f.), properties of c.d.f., concept of probability distribution. Uniform, exponential, Beta (I and II kind) and Normal distributions with their properties and applications. Normal distribution as limiting case of binomial and Poisson distribution (without proof). Unit-3 Lectures: 10 Transformation of univariate continuous and discrete r.v.s: Distribution of Y=g(X), where g is monotonic using (i) Jacobian of transformation (ii) Distribution function and (iii) m.g.f.

Unit-4 Lectures: 10 Meaning of ‘random sample from a distribution’, ‘statistic’, standard error, computation of sampling distribution of sum of random variables(discrete and continuous), CLT for iid (statement), Distribution of mean and variance from normal population. References


1. Hogg R.V. and Criag A.T.: Introduction to Mathematical Statistics (Third edition), Macmillan Publishing, New York.

2. Walpole R.E. & Mayer R.H.: Probability & Statistics, MacMillan Publishing Co. Inc, New York 3. Mayer P.L.: Introductory probability & Statistical Applications. Addison Weseley Publication

Co., London. 4. Goon A.M., Gupta A.K. and Dasgupta B.: Fundamentals of Statistics (Vol. II) World Press,

Calcutta. 5. Mukhopadhyay P. (1996): Mathematical Statistics, New central Book Agency (P) Ltd. Calcutta.

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PAPER CODE BST 202 PAPER NAME Practicals based on BST 201 CREDIT 01 (0-0-1) Total hours 45 CONTENT Students will be required to do practicals, based on topics listed below, using MS Excel:

1. Sketching of p.m.f., d.f. of Binomial and Poisson distributions 2. Sketching of p.d.f., d.f. of exponential, Beta (I and II kind) and Normal distributions

distributions 3. Fitting/Application of Binomial and Poisson distributions 4. Fitting/Application of exponential, Beta (I and II kind) and Normal distributions 5. Computation of Mean, Median, Mode, Range, Quartile, Interquartile Range and Variance for

the above distributions 6. Computation of probabilities corresponding to Uniform, Exponential, Beta, Normal

Distribution 7. Simulation of data from discrete and continuous distributions 8. Sampling Distribution of mean and Variance 9. Distribution of Y=g(X)

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PAPER CODE BST 203 PAPER NAME Statistical Inference –I CREDIT 04 (3-1-0) TOTAL HOURS 44 Unit-1 Lectures: 12 Concept of Statistical inference, sampling method and complete enumeration, Definition of population, parameter, parameter space, problem of estimation: point, intervals and testing of hypotheses. Definitions of an estimator, mean squared error (MSE) of an estimator, comparison of estimators based on MSE function. Unbiasedness: Unbiased estimator, Illustration of unbiased estimator for the parameter and parametric function. Definitions of Consistency, Sufficient condition for consistency, concept of efficiency and sufficiency. Neyman- Factorization theorem (without proof) Unit-2 Lectures: 8 Methods of estimation: Methods of moments, concept of likelihood function, Maximum Likelihood, Properties of MLE (without proof), Estimation of the parameters of normal distribution and other standard distributions by MLE. Unit-3 Lectures: 14 Hypothesis, types of hypothesis, problems of testing of hypothesis, critical region, type I and type II errors, probabilities of type I & type II errors. Power of a test, observed level of significance, p-value, size of a test, level of significance, testing for the mean and variance of Univariate normal population, testing of equalities of two means and variances of two Univariate normal populations. Definition of Most Powerful (MP) test, Neyman - Pearson (NP) lemma for simple null hypothesis against simple alternative hypothesis (proof), Examples of construction of MP test of level α, Testing hypotheses related to parameters of normal distribution including when both the parameters are unknown, Power curve of a test. Unit-4 Lectures: 10 Notion of non-parametric statistical inference (test) and its comparison with parametric statistical inference, Run test for one and two independent sample problems. Sign test for one sample and two sample paired observations, Wilcoxon's signed rank test for one sample and two sample paired observations, Mann-Whitney U - test (two independent samples), Kolmogorov Smirnov test for one and for two independent samples. References

1. George Casella, Roger L. Berger (2002), Statistical Inference, 2nd ed., Thomson Learning. 2. Mukhopadhyay P. (1996): Mathematical Statistics, New central Book Agency (P) Ltd. Calcutta. 3. Rohatgi, V.K. (1984): An Introduction to Probability Theory and Mathematical Statistics, Wiley

Eastern. 4. Goon, Gupta & Das Gupta (1991): An Outline of Statistical Theory, Vol. II, World Press. 5. Hogg, R.V. and Craig, A.T. (1971): Introduction to Mathematical Statistics, McMillan.

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PAPER CODE BST 204 PAPER NAME Practicals based on BST 203 CREDIT 01(0-0-1) TOTAL HOURS 45 CONTENT Students will be required to do practicals, based on topics listed below, using MS Excel:

1. Point estimation by Method of moments and maximum. 2. Mean squared error and unbiasedness of an estimator 3. Sketching of power curve 4. Testing of simple hypothesis against simple alternative hypothesis (Finite valued

discrete distributions, mean and variance of normal population). 5. Sign test for one sample and two samples 6. Wilcoxon's signed rank test for one sample and two samples 7. Run test (for one and two independent samples) and Sign test and Wilcoxon’s signed

rank test (for one and two samples paired observation). 8. Mann-whitney U- test (for two independent samples) and Median test (for two large

independent samples) 9. Kolmogorov-Smirnov test (for one and two independent samples).

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PAPER CODE BST 301 PAPER NAME Probability Distributions -II CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 12 Exact sampling distributions: Chi square distribution, Student’s t- distribution and Snedecor’s F distribution. Definitions, derivation of p.d.fs, sketch of p.d.fs. for various values of parameter, moments. Inter relation between t, F and χ2 (without proof). Applications of t, F and χ2 distributions. Laplace (Double Exponential) Distribution, Gamma distribution, Lognormal Distribution and Cauchy Distribution. P. d. f., Nature of the probability curve, Moments. Unit-2 Lectures: 10 Negative Binomial Distribution: p.m.f., mean, variance, m.g.f., geometric distribution is a particular case of Negative Binomial distribution., Recurrence relation for successive probabilities. Limiting property of the Negative Binomial Distribution. Hypergeometric Distribution: p.m.f., Computation of probabilities of different events, mean, variance, Recurrence relation for successive probabilities, Binomial approximation to Hypergeometric. Multinomial distribution: P.m.f., marginal distributions, m.g.f. Unit-3 Lectures: 13 Order statistics: definition, Derivation of p. d. f. of ith order statistics, for a random sample of size n from a continuous distribution. Density of smallest and largest observations. Distribution of the sample median when n is odd. Derivation of joint p. d. f. of ith and jth order statistics, statement of distribution of the sample range. Unit-4 Lectures: 10 Discrete and continuous bivariate random variables: Definitions, computation of probabilities of various events, marginal, conditional, product moments and correlations. Conditional expectation and conditional variance. The p. d. f. of a bivariate normal distribution, Marginal and conditional distributions, conditional expectation and conditional variance, regression of Y on X and of X on Y., independence and uncorrelated-ness imply each other, m. g. f and moments. Distribution of aX + bY + c, where a, b and c are real numbers. Plotting of bivariate normal density function. References


2. Hogg R.V. and Criag A.T.: Introduction to Mathematical Statistics (Third edition), Macmillan Publishing, New York.

3. Walpole R.E. & Mayer R.H.: Probability & Statistics, MacMillan Publishing Co. Inc, New York 4. Mayer P.L.: Introductory probability & Statistical Applications. Addison Weseley

Publication Co., London. 5. Goon A.M., Gupta A.K. and Dasgupta B.: Fundamentals of Statistics (Vol. II) World Press,

Calcutta. 6. H. A. David, H. N. Nagaraja, Order Statistics, Third Edition, John Wiley & Sons, Inc

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PAPER CODE BST 302 PAPER NAME Sample Survey CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 Basic concept: Elementary units, sampling frame, random and non-random sampling. Sampling, census advantages of sampling, Questionnaire and its characteristics. Simple random sampling: Simple random sampling from finite population of size N with replacement (SRSWR) and without replacement (SRSWOR): Definitions, population mean and population total as parameters, inclusion probabilities. Sample mean as an estimator of population mean, derivation of its expectation. Estimation of population proportion: Sample proportion (p) as an estimator of population proportion (P), derivation of its expectation, using SRSWOR. Determination of the sample size. Unit-2 Lectures: 15 Real life situations where stratification can be used, Description of stratified sampling method where sample is drawn from individual stratum using SRSWOR method. Estimator of population mean, population total, derivation of its expectation. Problem of allocation: Proportional allocation, Neyman’s allocation and optimum allocation, derivation of the expressions for the standard errors of the above estimators when these allocations are used. Gain in precision due to stratification, comparison with SRSWOR, stratification with proportional allocation and stratification with optimum allocation. Cost and variance analysis in stratified random sampling Unit-3 Lectures: 11 Systematic Sampling: Real life situations where systematic sampling is appropriate, Technique of drawing a sample using systematic sampling, Estimation of population mean and population total, Comparison of systematic sampling with SRSWOR and stratified sampling in the presence of linear trend. Idea of Circular Systematic Sampling. Cluster Sampling: Real life situations where cluster sampling is appropriate, Technique of drawing a sample using cluster sampling, Estimation of population mean and population total (with equal size clusters) Unit-4 Lectures: 9 Ratio Method: Concept of auxiliary variable and its use in estimation, Situations where Ratio method is appropriate, Ratio estimators of the population mean and population total and their standard errors (without derivations), Relative efficiency of ratio estimators with that of SRSWOR. Regression Method: Situations where Regression method is appropriate, Regression estimators of the population mean and population total and their standard errors (without derivations). References

1. Cochran, W.G: Sampling Techniques, Wiley Eastern Ltd., New Delhi. 2. Sukhatme, P.V., Sukhatme, B.V. and Ashok A. : Sampling Theory of Surveys with

Applications, Indian Society of Agricultural Statistics, New Delhi. 3. Murthy, M.N: Sampling Methods, Indian Statistical Institute, Kolkata. 4. Daroga Singh and Choudhary F.S.; Theory and Analysis of Sample Survey Designs,Wiley

Eastern Ltd., New Delhi. 5. Mukhopadhay, Parimal: Theory and Methods of Survey Sampling, Prentice Hall.

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PAPER CODE BST 303 PAPER NAME Time Series & Index Numbers CREDIT 04 (3-1-0) Total hours 45 Unit-1 Lectures: 5 Type of data in association with auto correlation, types of dependency, test of independency Unit-2 Lectures: 20 Meaning and utility of index numbers, problems in construction of index numbers. Types of index numbers: price, quantity and value, unweighted and weighted index numbers using (i) aggregate method, (ii) average of price or quantity relative method (A.M. or G.M. is to be used as an average). Index numbers using; Laspeyre’s, Paasche’s and Fisher’s formula. Tests of index numbers: unit test, time reversal test and factor reversal test. Cost of living index number: definition, problems in construction, construction by using (i) Family Budget and (ii) Aggregate expenditure method. Shifting of base, splicing, deflating and purchasing power of money. Uses of index numbers. Unit-3 Lectures: 20 Meaning and need of time series analysis, components of time series, additive and multiplicative model, utility of time series, concepts of autocorrelation and homoscadicityity and heteroscedasticity (without prof), preliminary concept of linear and non-linear time series.

References 1. Mukhopadhyay, P.:Applied Statistics, new Central Book Agency Pvt. Ltd., Calcutta. 2. Goon A.M., Gupta M.K. and Das Gupta B.: Fundamentals of Statistics, Vol. II, World

Press, Calcutta. 3. Chatfield C.: The Analysis of Time Series, IInd Edision Chapman and Hall. 4. Box, G. E. P. and Jenkins, G. M.: Time Series Analysis – Forecasting and Control,

Holden – day, San Francisco.

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PAPER CODE BST 304 PAPER NAME Statistical Inference –II CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 20 Statement and proof of Cramer Rao inequality. Definition of Minimum Variance Bound Unbiased Estimator (MVBUE) of ϕ (θ), (statement only). Proof of the following results:

(i) If MVBUE exists for θ then MVBUE exists for ϕ (θ), if ϕ(.) is a linear function. (ii) If T is MVBUE for θ then T is sufficient for θ. Examples and problems.

Definition of MVUE, Procedure to obtain MVUE (statement only), examples. Minimum Variance Unbiased Estimator (MVUE) and Uniformly Minimum Variance Unbiased Estimator (UMVUE), complete sufficient statistic and uniqueness of UMVUE whenever it exists. Unit-2 Lectures: 20 Review of testing of hypothesis and examples of construction of MP test of level α for binomial, Poisson, uniform, exponential and normal models. Testing for one sided and two sided alternatives: Power function of a test, Monotone likelihood ratio properties, definition of uniformly most powerful (UMP) level α test. Statement of the theorem to obtain UMP level α test for one-sided alternative. Illustrative examples. Likelihood Ratio Test (LRT) and its properties: LRT for (i) mean and variance of normal population. (ii) The difference of two means and ratio of two variances of normal populations. Unit-3 Lectures: 05 The need and the concept of confidence interval, Pivotal method of confidence interval, Confidence interval for proportion, mean and variance of normal distribution. Large sample Confidence interval. References

1. George Casella, Roger L. Berger (2002), Statistical Inference, 2nd ed., Thomson Learning. 2. Mukhopadhyay P. (1996): Mathematical Statistics, New central Book Agency (P) Ltd.

Calcutta. 3. Rohatgi, V.K. (1984): An Introduction to Probability Theory and Mathematical Statistics,

Wiley Eastern. 4. Goon, Gupta & Das Gupta (1991): An Outline of Statistical Theory, Vol. II, World Press. 5. Hogg, R.V. and Craig, A.T. (1971): Introduction to Mathematical Statistics, McMillan.

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PAPER CODE BST 305 PAPER NAME Numerical Analysis CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 Finite difference theory, basic property, forward and backword difference operators, Difference table(forward and backword), Displacement operator, Properties of operators, and E, nth difference of )(xPn , Difference of some special functions such as Trigonometrical, Exponential, Logarithmic, Relation between E and and E and , Method of separation of symbols, Factorial polynomial. Difference of a factorial polynomial.

Unit-2 Lectures: 10 Interpolation with equal interval: Interpolation meaning, assumptions and accuracy, method of interpolation, Newton’s Gregory forward and backword interpolation formulae for equal intervals, Newton’s advancing difference formula. Applications of Newton’s formula, Estimate of missing value of f(x) with the help of known values. Binomial expansion method (only one or two missing values). Unit-3 Lectures: 12 Interpolation with unequal intervals: Divided differences with divided difference table, Properties of divided differences, Newton’s divided difference formula, Relation between divided and ordinary differences. Lagrange’s Interpolation formula. Central difference formulae due to Gauss (Forward and backword),Sterling’s formula, Bessel’s formula.

Unit-4 Lectures: 13 Numerical Integration: General Quadrature formula, Trapezoidal rule, Simpson’s one third and three eight rules, Weddle’s rule, Eular Maclaurin’s summation formula and its application. Solution of algebraic and transcendental equations synthetic division method, graphical method Regula falsi method, Newton’s Raphson method. Solution of ordinary difference equations (first order), Eular’s methods Eular’s modified method, Picard’s methods. References

1. Operation Research by Kantiswaroop, P. K. Gupta & Man Mohan. 2. Numerical methods: problems and solutions by Jain, Iyengar and Jain, New Age

International Publisher. 3. An introduction to numerical analysis (2nd Edition) by K.E. Atkinson, John Wiley, 1989. 4. Numerical methods and analysis by J.I. Buchanan and P.R. Turner, McGraw-Hill, 1992. 5. Numerical analysis, Bansal and Ojha, Jaipur publishing house Jaipur.

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PAPER CODE BST 306 PAPER NAME Practicals CREDIT 04 (0-0-4) TOTAL HOURS 45 CONTENT Students will be required to do practicals, based on topics listed below, using MS Excel, :

1. Model sampling from Gamma and log normal distributions. 2. Sketching of p.m.f., d.f. of Negative Binomial and Hypergeometric distributions 3. Bivariate Discrete distribution – I (Marginal & conditional distribution, computation of

probabilities of events. Expectations/conditional expectations/ variances / conditional variance/covariance /correlation coefficient)

4. Model sampling from bivariate normal distribution and Application of bivariate normal distribution.

5. Simple random sampling with and without sampling 6. Stratified random sampling. 7. Systematic Sampling. 8. Ratio Method of Estimation. 9. Regression Method of Estimation. 10. Determination of secular trend by moving averages and least squares methods. 11. Construction of index numbers. 12. Tests for consistency of index numbers. 13. Construction of Consumer Price Index - interpretation. 14. Interval estimation of location and scale parameters of normal distribution and population

proportion Interval estimation for difference between two population proportions. 15. Likelihood ratio test 16. General quadrature formulae and Missing values 17. Newton’s Gregory forward and backword interpolation (equal interpolation)

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PAPER CODE BST 351 PAPER NAME Elements of Reliability & Survival Analysis CREDIT 04 (3-1-0) TOTAL HOURS 44 Unit-1 Lectures: 10 Preliminaries: Definition and concept of time, event, Survival function, quantiles, hazard rate, cumulative hazard function and their relation with survival function mean residual life. Parametric models: Exponential, Weibull and normal and their survival characteristics. Unit-2 Lectures: 12 Censoring mechanisms- type I, type II and left right and interval censoring. Likelihood function under censoring, Fitting parametric models to survival data without censoring and with right censoring. Unit-3 Lectures: 12 System and its Configuration, Series Configuration, Parallel Configuration, Series -Parallel Configuration, Parallel - Series Configuration.

Unit-4 Lectures: 10 Empirical survival function, Actuarial estimator, Kaplan–Meier estimators and its properties. References

1. Deshpande, J.V. and Purohit, S. G.(2005): Life Time Data: Statistical Model and Methods, World Scientific.

2. Cox, D. R. and Oakes, D. (1984): Analysis of Survival Data, Chapman and Hall, New York. 3. Sinha, S. K. and Kale, B. K. (1983): Life Testing and Reliability Estimation, Wiley

Eastern Limited. 4. Elandt – Johnson, R.E. Johnson N. L.: Survival Models and Data Analysis, John Wiley and

Sons. 5. Miller, R. G. (1981): Survival Analysis (John Wiley)

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PAPER CODE BST 352 PAPER NAME Design of Experiments CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Introduction, One factor analysis, the model and problem Decomposition of total sum of squares, independence of decomposed sum of squares, ANOVA table, two factor analysis ANOVA table, Test for normality. Basic terms in design of experiments: Experimental unit, treatment, layout of an experiment. Basic principles of design of experiments: Replication, randomization and local control. Choice of size and shape of a plot for uniformity trials, the empirical formula for the variance per unit area of plots. Unit-2 Lectures: 15 Complete randomized design, randomized block design and Latin square design. Layout, model, assumptions and interpretations: Estimation of parameters, expected values of mean sum of squares, components of variance. Tests and their interpretations, test for equality of two specified treatment effects, comparison of treatment effects using critical difference (C.D.). Efficiency of design: Concept and definition of efficiency of a design. Efficiency of RBD over CRD. Efficiency of LSD over CRD and LSD over RBD. Identification of real life situations where CRD, RBD and LSD are used. Unit-3 Lectures: 15 General description of factorial experiments, 22 and 23 factorial experiments arranged in RBD. Definitions of main effects and interaction effects in 22 and 23 factorial experiments. Model, assumptions and its interpretation. General idea and purpose of confounding in factorial experiments. Total confounding (Confounding only one interaction): ANOVA table, testing main effects and interaction effects. Construction of layout in total confounding, confounding in 23 factorial experiments. References

1. Goon, Gupta, Dasgupta : Fundamental of Statistics, Vol. I and II, The World Press Pvt. Ltd. Kolkata.

2. Montgomery, D.C.: Design and Analysis of Experiments, Wiley Eastern Ltd., New Delhi. 3. Cochran, W.G. and Cox, G.M.: Experimental Design, John Wiley and Sons, Inc., New York. 4. Gupta, S.C. and Kapoor, V.K. : Fundamentals of Applied Statistics, S. Chand & Sons, New

Delhi. 5. Das, M.N. and Giri, N.C. : Design and Analysis of Experiments, Wiley Eastern Ltd., New Delhi.

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PAPER CODE BST 353 PAPER NAME Statistical Process Control & Vital Statistics CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 Meaning and purpose of Statistical Process Control, Concept of Quality and Quality Control, process control, product control, assignable causes, chance causes and rational subgroups Unit-2 Lectures: 15 Control charts and their uses, Choice of subgroup sizes, Construction of control chart for തܺ (mean), ܴ (range), ݏ (standard deviation), ܿ (no. of defectives), (fraction defectives) with unequal subgroup size. Interpretation of non-random patterns of points. Modified control chart. Unit-3 Lectures: 10 Census, Registrar, Ad-hoc surveys, Hospital records, Demographic profiles of the Indian census. Crude death rate, Age-specific death rate, Infant mortality rate, Death rate by cause, standardized death rate. Central Mortality Rate, Force of Mortality Rate. Unit-4 Lectures: 10 Description and construction of complete and abridged life tables and their uses. Construction of complete life table from population and death statistics. Stable and Stationary populations. References

1. Mukhopadhyay, P. (1994): Applied Statistics, new Central Book Agency Pvt. Ltd., Calcutta.

2. Goon A.M., Gupta M.K. and Das Gupta B. (1986): Fundamentals of Statistics, Vol. II, World Press, Calcutta.

3. Srivastava, O.S. (1983) : A text book of demography. Vikas Publishing House, New Delhi.

4. Duncan A.J. (1974) : Quality Control and Industrial Statistics, IV Edision, Taraporewala and Sons.

5. Benjamin, B. (1959) : Health and vital statistics. Allen and Unwin

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PAPER CODE BST 354 PAPER NAME Operation Research CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Nonlinear Programming: Unconstrained algorithms; direct search method, gradient method. Constrained methods; Separable programming, quadratic programming. General Inventory models, role of demand in the development of inventory; Static Economic-Order-Quantity (EOQ) models; Dynamic EOQ models. Continuous review model, single period models, multi period models. Unit-2 Lectures: 15 Elements of Queuing models, role of exponential, pure birth and death models. Generalized Poisson Queuing models, Specialized Poisson Queues: Steady state measures of performance, single server model multi server models, machine servicing models-(M/M/R): (GD/K/K), R< K. Replacement and maintenance models; gradual failure, sudden failure, replacement due to efficiency deteriorate with time, staffing problems, equipment renewal problems. Unit-3 Lectures: 15 Simulation modeling: Monte Carle Simulation, Types of simulations, Elements of discrete-events simulation, generation of random numbers. Mechanics of discrete simulation, Methods of gathering statistical observations: subinterval method, replication method, regeneration method. Sequencing Problems: notions, terminology, and assumptions, processing n jobs through m machines.

References 1. Operations Research an Introduction –Hamady A. Taha, Prentice Hall. 2. Operations Research Theory and Applications-J. K. Sharma, Macmillan Publishers. 3. Non linear Programming –S.D. Sharma, Kedar Nath Ram Nath & Co. 4. Mathematical Programming Theory and Methods-S.M.Sinha. 5. Operations Research, - Kanti Swarup, P. K. Gupta and Man Mohan, Sultan Chand & Sons.

Annexure-I


PAPER CODE BST 355 PAPER NAME Official Statistics & Demand Analysis CREDIT 04 (3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 8 Present official statistical system in India relating to census and population; methods of collection of official statistics. Various agencies responsible for the data collection: Central Statistical Organization (CSO), the National Sample Survey Organization (NSSO), office of Registrar General, their main functions and important publications. State Government organizations. Unit-2 Lectures: 7 Agricultural Statistics: Area and Yield statistics. National Income statistics: Income, expenditure and production approaches. Their applications in various sectors in India. Unit-3 Lectures: 15 Demand Analysis: Introduction, Necessities and Luxuries, Demand and Supply, Laws of Demand and Supply: Demand and Supply Curve. Price Elasticity of Demand: Significance of Elasticity of Demand, Demand Function with constant price elasticity. Price Elasticity of Supply: Supply Curve with the constant Price Elasticity. Partial Elasticities of Demand.

Unit-3 Lectures: 15 Types of Data Required for Estimating Elasticities: Family Budget Data (cross section data) and Market Statistics or Time Series Data. Methods of Estimating Demand Function: Leontief’s Method and Pigous’s Method. Engel’s Law and Engel’s Curve. Pareto’s Law of Income Distribution. Utility Function. References

1. Gupta S. C. and Kapoor V. K. (2008): Fundamentals of Applied Statistics. 4th Edn. (Reprint) Sultan Chand & Sons, New Delhi.

2. C. S. O. (1984): Statistical System in India. 3. Goon A. M.,Gupta M. K,, and Dasgupta. B. (2005): Fundamentals of Statistics. Vol.-II, 8th

Edn. World Press, Kolkata. 4. Mukhopadhyay P. (1999): Applied Statistics. Books and Allied (P) Ltd. 5. Nagar A. L. & Das R. K. (1976): Basic Statistics 6. Elhance, D. N. and Elhance, V. (1996): Fundamentals of Statistics. D.K. Publishers. 7. M.R.Saluja : Indian Official Statistics. ISI publications.

Annexure-I


PAPER CODE BST 356 PAPER NAME Practicals CREDIT 04 (3-1-0) TOTAL HOURS 45 CONTENT Students will be required to do practicals, based on topics listed below, using MS Excel, :

1. Analysis of CRD. 2. Analysis of 22 factorial experiment using RBD layout. 3. Analysis of 23 factorial experiment using RBD layout. 4. Analysis of 23 factorial experiment using RBD layout. (Complete confounding) 5. Markov Chains: realizations, classification of states. 6. Poisson process: realizations, examples 7. Computation of various mortality and fertility rates. 8. Construction of life table and computation of expectation of life and force of mortality. 9. Plotting of survival function, hazard rate for probability distributions. 10. Kaplan-Meier Estimator. 11. Demand and Supply Curve 12. Analysis of demographic data (India) 13. Analysis of agricultural data (India) 14. തܺ–R charts. (Standard values known and unknown) 15. np and p charts. (Standard values known and unknown). 16. Laws of Income Distributions 17. Linear programming (graphical methods) 18. Simplex method 19. Transportation problems.

Annexure-I


PAPER CODE MST 101 PAPER NAME Probability Theory CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 Random experiment, outcomes, sample space, the class of subsets (events), Borelfield(ᆓ-field), axiomatic definition of probability measure, combination of events. Bonferroni and Boole inequalities. Independence of events (pairwise and complete independence).Sequences of events.Borel-Cantelli lemma. Conditional probability, laws of total and compound probability, Bayes Theorem. Unit-2 Lectures: 15 Concept of a random variable on a finite probability space and its probability distribution.Probability mass function and cumulative distribution function (cdf) of a random variable.Extension of the concept to any discrete random var-iable and an absolutely continuous random variable. Unit-3 Lectures: 10 Expectation of a random variable, proper-ties of expectation, conditional expectation and its properties. Moments, quantiles, and variance.Properties of a cdf. Bivariate distributions and the joint probability distribution. Independence of random variables. Marginal and conditional distributions. Moment generating function, probability generating function, characteristic function and their properties.Inversion, continuity and uniqueness theorems. The moment problem.Demoivre-Laplace Central Limit Theorem, Central Limit Theorem for IID random variables, Central Limit Theorem. Unit-4 Lectures: 10 Sequences of random variables.Convergence in distribution and in probability. Almost sure convergence and convergence in the rth mean. Implication between modes of convergence.Slutsky’s theorem. Tchebychev and Khintchine weak laws of large numbers. Kolmogorov inequality(statement). Kolmogorov strong law of large numbers (statement). References

1. Bhat, B.R. (1999). Modern Probability Theory, 2/e, New Age International, New Delhi. 2. Rao B. L. S. Prakasa (2009) A First course in Probability and Statistics. World Scientific 3. Meyer, P.A. An Introduction to Probability and Its Applications. PHI 4. John E Freund (2004): Mathematical Statistics with applications. 7th ed. Upper saddle

River, NJ: Prentice Hall. ISBN: 0131246461. 5. Rohatgi V.K & A.K. MD. Ehsanes Saleh (2001): An Introduction to Probability Theory

andMathematical Statistics, 2nd. John Wiley and Sons.

Annexure-I


PAPER CODE MST 102 PAPER NAME Distribution Theory CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 8 Discrete Distributions: Binomial, Poisson, multinomial, hypergeometric, negative binomial, uniform. The (a,b,0) class of distributions. Moments, quantiles, cdf, survival function and other properties. Unit-2 Lectures: 15 Continuous Distributions: Uniform, Normal, Exponential, gamma, Weibull, Pareto, lognormal, Laplace, Cauchy, Logistic distributions; properties and applications. Functions of random variables and their distributions using Jacobian of transformation and other tools. Bivariate normal and bivariate exponential distributions. Unit-3 Lectures: 12 Concept of a sampling distribution. Sampling distributions of t, χ2 and F (central and non central), their properties and applications. Multivariate normal distribution. Distribution of a linear function of normal random variables. Characteristic function of the multivariate normal distribution. Distribution of quadratic forms. Cochran’s theorem. Independence of quadratic forms. Unit-4 Lectures: 10 Compound, truncated and mixture distributions. Convolutions of two distributions. Order statistics: their distributions and properties. Joint, marginal and conditional distribution of order statistics. The distribution of range and median. Extreme values and their asymptotic distribution (statement only) with applications. References

1. Rohatgi V.K & A.K. MD. Ehsanes Saleh: An Introduction to Probability Theory and Mathematical Statistics, 2nd. John Wiley and Sons, 2001.

2. Johnson, Kotz and Balakrishna, Continuous univariate distributions, Vol- 1 IInd Ed, John Wiley and Sons

3. Johnson, Kemp and Kotz, Univariate discrete distributions, IIInd Ed, John Wiley and Sons

4. Mukhopadhyay P. (1996): Mathematical Statistics, New central Book Agency (P) Ltd. Calcutta.

5. Goon, Gupta & Das Gupta (1991): An Outline of Statistical Theory, Vol. I, World Press.

Annexure-I


PAPER CODE MST 103 PAPER NAME Linear Algebra and Matrix Theory CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 12 Linear equations and matrices, matrix operations, solving system of linear equations, Gauss-Jordan method, Concept & Computation of determinant and inverse of matrix, Eigen values and eigen vectors, illustrations of the methods, Positive semi definite and position definite matrices, illustrations. Unit-2 Lectures: 12 Overview. Fields (real and complex numbers are special cases), and the notion of a vector space over a field. Subspaces. Sums and direct sums of subspaces. Criteria for a sum to be a direct sum. Examples. Linear combinations and spans. Finite dimensional vector spaces. Linear independence and the notion of basis. More on basis and dimension. Unit-3 Lectures: 13 More about the structure of linear maps on complex vector spaces: Jordan normal form. The minimal polynomial and relation to characteristic polynomial. Analogous (but weaker) results for linear maps on real vector spaces: existence of 1 or 2 dimensional invariant subspaces block upper triangular matrices, the characteristic polynomial of 2x2 matrices. Eigen pairs and generalized Eigen pair-spaces. Decomposition into generalized Eigen spaces and Eigen-pair spaces. Unit-4 Lectures: 8 More properties of the adjoint of a linear map between inner product spaces (behavior with respect to composition, sums and scalar products, kernels and images). Self-adjoint operators: first properties. Normal operators (a larger class than self-adjoint), and their characterization. The complex and real spectral theorems. References

1. Searle, S. R. (1982). Matrix Algebra Useful for Statistics; John Wiley, New York.

2. Ramachandra Rao, A. and Bhimasankaram, P. (1992): Linear Algebra, Tata McGrawhill.

3. Krishnamurthy V., Mainra V.P. and Arora J. L. (2009) An introduction to Linear Algebra,

East-West Press Pvt Ltd.

4. Rudin, W. (1985). Principles of Mathematical Analysis, McGrawhill, New York.

5. Malik, S.C. and Arora, S. (1998). Mathematical Analysis, New Age, New Delhi.

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PAPER CODE MST 104 PAPER NAME Sampling Theory CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 12 Concept of population and sample, Need for Sampling, census & sample surveys, basic concepts in sampling and designing of large-scale surveys design, sampling scheme and sampling strategy. Basic methods of sample selection: SRSWR, SRSWOR. Stratification, Allocation and estimation problems. Construction of Strata: deep stratification, method of collapsed strata. Unit-2 Lectures: 17 Systematic sampling: The sample mean and its variance, comparison of systematic with random sampling, comparison of systematic sampling with stratified sampling, comparison of systematic with simple and stratified random sampling for certain specified population. Estimation of variance, Two stage sample: Equal first stage units, Two stage sample: Unequal first stage units; systematic sampling of second stage units. Unequal probability sampling: PPSWR/WOR methods (including Lahiri’s scheme) and Des Raj estimator, Murthy estimator (n=2). Horvitz Thompson Estimator of a finite population total/mean, Midzuno sampling. Unit-3 Lectures: 11 Cluster sampling. Two – stage sampling with equal number of second stage units. Use of supplementary information for estimation: ratio and regression estimators and their properties. Unbiased and almost unbiased ratio type estimators, Double sampling. Unit-4 Lectures: 05 Non-sampling error with special reference to non-response problems. Hansen – Horwitz and Demig’s techniques. References

1. Sukhatme P. V., Sukhatme B. V.& Ashok C : Sampling Theory of surveys with applications – Indian Society of Agricultural Statistics, New Delhi.

2. Des Raj and Chandhok. P. (1998) : Sample Survey Theory - Narosa publication. 3. William G. Cochran. ( 1977) : Sampling Techniques- IIIrdedition –John and Wieley sons Inc. 4. Parimal Mukhopadhyay (1998) : Theory and methods of survey sampling –Prentice Hall of

India private limited. 5. Murthy M.N. (1977) : Sampling Theory of Methods - Statistical Publishing Society, Calcutta.

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PAPER CODE MST 105 PAPER NAME R: Statistical Programming Language CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 12 Introduction, installation, start and quite, help.search(), console and script, Saving workspace/history. Advantages, packages. Data handling in R: numeric/character/logical type data, real/integer/complex type data, matrices with their operations, data frames, lists, creating arrays/vectors. Arithmetic and logical operators, some mathematical expressions such as logarithm, square-root, exponentiation etc. data editor. Unit-2 Lectures: 10 Control structures: conditional statements - if and if else; loops - for, while, do-while; nested loops, functions – built-in and user defined, Import and export of excel and text sheets. Unit-3 Lectures: 10 High level, Low level and Interactive graphics, plot command, histogram, barplot, boxplot, Pie charts, inserting mathematical symbols in a plot, Customisation of plotsetting graphical parameters, adding text, saving to a file; Adding a legend. Unit-4 Lectures: 13 Descriptive statistics; mean, variance, correlation and summary statistics. Linear models: functions for ANOVA/regression. Test of significance; t tests, chi-square test, Nonparametric tests. Probability Distributions: Obtaining density, cumulative density and quantile values for discrete and continuous distributions; simulations from discrete and continuous distributions, Plotting density and cumulative density curves. References

1. Peter Dalgaard, Introductory Statistics with R, Springer, 2nd edition, 2008. 2. Michael J. Crawley, The R Book, John Wiley and Sons, Ltd., 2007. 3. Richard A. Becker, John M. Chambers and Allan R. Wilks (1988), The New S Language.

Chapman & Hall, New York. 4. John M. Chambers and Trevor J. Hastie eds. (1992), Statistical Models in S. Chapman & Hall,

New York. 5. John M. Chambers (1998) Programming with Data. Springer, New York.

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PAPER CODE MST 106 PAPER NAME Practicals CREDIT 04 (0-0-4) TOTAL HOURS 45 CONTENT Students will be required to do practicals, based on topics listed below, using R software:

1. Convergence of the random variable 2. Fitting of discrete and continuous distributions 3. Sketching of p.m.f./ pdf of discrete/ continuous distributions 4. R- program (User defined) for Matrix operations (Multiplication, determinate, inverse,

Eigen values and vector) 5. Simple random sampling with and without sampling 6. Stratified random sampling. 7. Systematic Sampling. 8. Ratio Method of Estimation. 9. Regression Method of Estimation. 10. Unequal probability sampling: PPSWR/WOR methods (including Lahiri’s scheme) 11. Cluster sampling

There shall be minimum two practical assignments from each optional course.

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PAPER CODE MST 201 PAPER NAME Estimation and Testing of Hypotheses CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 13 Concept of mean squared error, Criteria of a good estimator: unbiasedness, consistency, efficiency and sufficiency. Fisher-Neyman factorization theorem, Family of distributions admitting sufficient Statistic. Point estimation, Maximum likelihood method (MLE), moments, Least squares method. Method of minimum chi-square and percentiles. Properties of maximum likelihood estimator (with proof). Successive approximation to MLE, Method of scoring and Newton-Raphson method. Unit-2 Lectures: 10 Cramer-Rao inequality and its attainment, Cramer-Huzurbazar theorem (statement only), Completeness and minimal sufficient statistic, Ancillary statistic, Basu theorem, Uniformly minimum variance unbiased estimator (UMVUE). Rao-Blackwell and Lehmann-Scheffe theorems and their applications, Review of convergences of random variables and their implications, Delta method and its application, Asymptotic efficiency and asymptotic estimator, consistent asymptotic normal (CAN) estimator. Unit-3 Lectures: 12 Statistical Hypothesis, critical region, types of errors, level of significance, power of a test, Test function, Randomized and non-randomized tests, Most powerful test and Neyman-Pearson lemma. MLR family of distributions, unbiased test. Uniformly most powerful test. Uniformly most powerful unbiased test. Likelihood ratio test with its properties. Unit-4 Lectures: 10 Confidence interval, confidence level, construction of confidence intervals using pivots, Determination of confidence intervals based on large and small samples, uniformly most accurate one sided confidence interval and its relation to UMP test for one sided null against one sided alternative hypotheses. References

1. George Casella, Roger L. Berger, Statistical Inference, 2nd ed., Thomson Learning. 2. Mukhopadhyay P.: Mathematical Statistics, New central Book Agency (P) Ltd. Calcutta. 3. Rao, C.R.: Linear Statistical Inference and its Applications, 2nd ed, Wiley Eastern. 4. Rohatgi, V.K.: An Introduction to Probability Theory and Mathematical Statistics, Wiley

Eastern. 5. Mood, Graybill and Boes.: Introduction to the theory of Statistics 3rd ed., McGraw- Hill. 6. Goon, Gupta & Das Gupta: An Outline of Statistical Theory, Vol. II, World Press. 7. Hogg, R.V. and Craig, A.T.: Introduction to Mathematical Statistics, McMillan. 8. Kendall, M.G. and Stuart, A. : An Advanced Theory of Statistics, Vol. I,II. Charles Griffin. 9. Kale, B.K. : A First Course on Parametric Inference, Narosa Publishing House. 10. Lehmann, E.L.: Testing Statistical Hypotheses, Student Editions.

Annexure-I


PAPER CODE MST 202 PAPER NAME Linear Models CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Theory of linear estimation, Estimable function, Simple linear regression, multiple regression model, least squares estimation, variance and covariance of least squares estimator, Gauss-Markov theorem in linear estimation. Unit-2 Lectures:10 Interval Estimation for regression coefficients 0, 1 and 2, Interval estimation of the linear functions of . Interval estimation of the mean response, simultaneous confidence intervals. The R2 statistic. Hypothesis testing for model adequacy, testing of sub hypothesis. Test of hypothesis for a linear parametric function. Point and interval prediction. Unit-3 Lectures: 10 Fundamental concept of generalized linear model (GLM), exponential family of random variables. Link functions such as Logit, Probit, binomial, inverse binomial, inverse Gaussian, gamma. Non linear models, ML estimation in non linear models. Unit-4 Lectures: 10 Diagnostic checks for suitability and validation of a linear regression model, graphical techniques, tests for normality, linearity, uncorrelated ness, multicollinearity, lack of fit, Cp criterion. Ridge regression, outliers and influential observations. Stepwise, forward and backward procedures for selection of best sub-set of regressors. References

1. Montgomery, Douglas C.; Peck, Elizabeth A.; Vining, G. Geoffrey: (2003) Introduction to Linear Regression Analysis. John Wiley and sons.

2. Draper, N. R. & Smith, H(1998) Applied Regression Analysis, 3rd Ed., John Wiley.. 3. Dobson, A. McCullagh, P & Nelder, J. A. (1989) Generalized Linear Models, Chapman

& Hall. 4. Ratkowsky, D.A. (1983) Nonlinear Regression Modelling (Marcel Dekker). 5. Hosmer, D.W. & Lemeshow, S. (1989) Applied Logistic Regression (John Wiley). 6. Seber, G.E.F. and Wild, C.J. (1989) Nonlinear Regression (Wiley) 7. Neter, J., Wasserman, W., Kutner, M.H. (1985) Applied Linear Statistical Models.

(Richard D. Irwin). 8. Rao.C.R(1973).:Linear statistical Inference and its application. 9. Goon, A.M., Gupta, M.K. and Das Gupta, B. (1967): An Outline of Statistical Theory,

Vol. 2

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PAPER CODE MST 203 PAPER NAME Stochastic Models CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Definition and examples of stochastic process: Classification of general stochastic processes into discrete/continuous time, discrete/continuous state spaces, elementary problems, Random walk and Gambler's ruin problems, Counting process, Time series model.

Unit-2 Lectures:10 Markov chains: Definition and examples of Markov Chain, Transition probability matrix, classification of states, communicating classes, recurrence: non-recurrence, Irreducibility, Stationary distribution and its interpretation, Chapman-Kolmogorov equation, Stationary probability distribution, applications. Computation of n-step transition probability matrix by spectral representation. Absorption probability and mean time to absorption. Unit-3 Lectures: 10 Continuous time Markov Chain: Poisson process and related inter-arrival time distribution, compound Poisson process, Pure birth process, pure death process, birth and death process, problems, Renewal processes, Elementary renewal theorem and its applications. Unit-4 Lectures: 10 Galton -Watson branching processes: Definition and examples of discrete time branching process, Probability generating function and its properties, Offspring mean and probability of extinction. Introduction to Brownian motion process and its basic properties. Applications to insurance problems. References

1. Kulkarni, Vidyadhar: Modeling and Analysis of Stochastic systems, G. Thomson Science and Professional.

2. Ross, S.: Introduction to Probability Models,6th Ed., Academic Press. 3. Bhat, B.R.:. Stochastic Models: Analysis and Applications, (2nd New Age International,

India). 4. Medhi J. : Stochastic processes, new Age International (P) Ltd. 5. Karlin S. and Taylor H.M. : A First Course in Stochastic Process, Academic Press 6. Hoel P.G., Port S.C. and Stone C.J.:Introduction to Stochastic Process, Universal Book Stall. 7. Parzen E. : Stochastic Process, Holden-Day 8. Cinlar E. Introduction to Stochastic Processes, Prentice Hall. 9. Adke S.R. and Manjunath S.M.:An Introduction to Finite Markvo Processes, Wiley Eastern. 10. Ross S.M.: Stochastic Process, John Wiley. 11. Taylor H.M. and Karlin S.: Stochastic Modeling, Academic Press. 12. John G. Kemeny, J. Laurie Snell, Anthony W. Knapp: Denumerable Markov Chains.

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PAPER CODE MST 206 PAPER NAME Practicals CREDIT 04 (0-0-4) Total hours 45 CONTENT Students will be required to do practicals, based on topics listed below, using R software:

1. Construction of life tables and Problems based on life tables 2. Life table using analytical laws of mortality(Makeham’s model and Gompertz’s model) 3. Life Annuity immediate and due. 4. Calculation of premiums. 5. Calculation of reserves. 6. Linear Estimation. 7. Test of hypotheses for one and more than one linear parametric functions. 8. Multiple Regression 9. Estimation of regression coefficient, Fitting of multiple linear regression. 10. Testing of hypothesis concerning regression coefficient. 11. Testing of significance of association between the dependent and independent variable 12. Non-linear regression. 13. Logistic Regression. 14. Plotting likelihood functions for standard probability distributions. 15. Moment Estimation, Maximum Likelihood Estimation (for discrete, continuous, mixture,

truncated distributions.) 16. MP test 17. Calculation of n-step transition probabilities and limiting distribution in Markov chain. 18. Realization of Markov chain. 19. Estimation of transition probability of Markov chain using realization.

There shall be minimum two practical assignments from each optional course.

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PAPER CODE MST 221 PAPER NAME Design of experiment –II CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 12 Basic principle of experimental design, overview of RBD, CRD and LSD, Missing plot techniques in RBD with one and two missing observations, Analysis of LSD with one missing observation. Unit-2 Lectures:11 General theory of intra block analysis of block design, connectedness and balancing block design, incomplete block design, intra block analysis of BIBD and its properties. Unit-3 Lectures: 12 Purpose of analysis of covariance. Practical situations where analysis of covariance is applicable. Model for analysis of covariance in CRD and RBD. Estimation of parameters (derivations are not expected).Preparation of analysis of covariance (ANOCOVA) table, test for β = 0, test for equality of treatment effects (computational technique only). Unit-4 Lectures: 10 General description of factorial experiments, factorial effects, analysis of factorial experiment (2n, 3n), main and interaction effects, advantages and disadvantages, total and partial confounding, split plot experiment. References

1. Goon, Gupta, Dasgupta : Fundamental of Statistics, Vol. I and II, The World Press Pvt. Ltd. Kolkata.

2. Montgomery, D.C.: Design and Analysis of Experiments, Wiley Eastern Ltd., New Delhi. 3. Cochran, W.G. and Cox, G.M.: Experimental Design, John Wiley and Sons, Inc., New York. 4. Gupta, S.C. and Kapoor, V.K. : Fundamentals of Applied Statistics, S. Chand & Sons, New

Delhi. 5. Das, M.N. and Giri, N.C. : Design and Analysis of Experiments, Wiley Eastern Ltd., New Delhi. 6. Joshi, D. D.: Linear estimation and design of experiment. 7. Dey, Alok: Theory of block designs, Wiley Eastern.

Annexure-I


PAPER CODE MST 222 PAPER NAME Econometrics CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Introduction of Econometrics, Multiple Linear Regression Model, Model with non-spherical disturbances, Test of Auto-correlation, restricted regression estimator, Errors in variables, Dummy variables, Logit and Probit Models Unit-2 Lectures:10 Seemingly unrelated regression equation (SURE) model and its Estimation, Simultaneous equations model, concept of structural and reduced forms problem of identification, rank and order condition of identifiability. Unit-3 Lectures: 10 Methods of estimation of simultaneous equation model: indirect least squares, two stage least squares and limited information maximum likelihood estimation, idea of three stage least squares and full information maximum likelihood estimation, and prediction Unit-4 Lectures: 10 Panel data models: Estimation in fixed and random effect models, Panel data unit root test References

1. Apte, P.G.: Text books of Econometrics, Tata McGraw Hill. 2. Gujarathi, D.: Basic Econometrics; McGraw Hill. 3. Johnston, J.: Econometrics Methods. Third edition, McGraw Hill. 4. Srivastava, V.K. and Giles D. A. E.: Seemingly unrelated regression equations models, Marcel

Dekker. 5. Ullah, A. and Vinod, H.D.: Recent advances in Regression Methods, Marcel Dekker.

Annexure-I


PAPER CODE MST 223 PAPER NAME Financial Mathematics CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Accumulation Function, Simple interest, compound interest, Generalized Cash- flow model, Concepts of compound interest and discounting, Nominal Interest rates or discount rates in terms of different time periods, Force of interest Unit-2 Lectures:12 Definition of compound interest functions including annuities certain, Level payment annuities, Level payment perpetuities, Repayment mode (mthly), Non-level payment annuities and perpetuities: Geometric, Increasing and Decreasing, Continuous payment Cashflows Unit-3 Lectures: 10 The investment and risk characteristics of the different types of asset available for investment purposes, Variable interest rates, Investment and risk characteristics of various types of assets such as bonds, shares, options and derivatives. Unit-4 Lectures: 8 Forwards, Future, Call options, Put options, Put-call parity and swap, Structure of interest rates, Simple stochastic models for investment returns. References

1. Hull, J. C., (2003) Derivatives Options & Futures, Pearson Education. 2. Donald D.W.A. (1984). Compound Interest & Annuities Certain. Published for the Institute of

Actuaries and the Faculty of Actuaries, London. 3. Mark Suresh Joshi,(2009) The Concept and Practice of Mathematical Finance, Cambridge

University Press. 4. Dixit S. P., Modi C.S. and Joshi R.V. (2000). Mathematical Basis of Life Assurance. Published

by Insurance Institute of India, Bombay. 5. Kellison, Stephen G(1991) The Theory of Interest, Homewood, IL: Richard D. Irwin, 2nd ed.

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PAPER CODE MST 224 PAPER NAME Economics for Actuarial Science CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Economic concepts, Demand and supply, Elasticity and uncertainty, Consumer demand and uncertainty, Production and costs, Revenue and profit. Unit-2 Lectures:10 Perfect competition and monopoly, Imperfect competition, Growth strategy and globalization, Pricing strategies Unit-3 Lectures: 10 Government intervention in markets, Government and the firm, Supply-side policy, International trade, Balance of payments and exchange rates Unit-4 Lectures: 10 The macroeconomic environment, Money and interest rates, Business, unemployment and, Inflation, Demand-side macroeconomic policy References

1. John Sloman and Kevin Hinde:Economics for Business, 4th ed. 2. Begg David, Stanley Fischer and Rudiger Dornbusch :Economics (7th ed.) and 3. Economics workbook, McGraw Hill ISBN: 0077099478. 4. Samuelson Paul and Willian Norhaus :Economics, 16th ed., McGraw Hill. 5. Mankiw, N.G.; Taylor, M.P. Thomson :Economics. ISBN: 1844801330 6. Parkin, M.; Powell, M.; Matthews, K. :Economics, 6th ed., Pearson Education,. ISBN:

0321312643. 7. Wonnacott P. and R. Wonnacott :Economics, 4th ed. John Wiley. 8. Gwartney James D. and Richard L. Stroup: Economics: Private and Public choice (8th ed. )

HBJ College & School Division. 9. Lipsey Richard G. and Chrystat K. Alec :Principles of Economics, Oxford University Press. 10. Institute of Actuaries core reading for the subject CT7-Economics

Annexure-I


PAPER CODE MST 225 PAPER NAME Machine Learning CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 An overview of Machine learning, Inductive learning: ID3, C4.5,C5; Learning Concepts and rules from Examples; Learning by analogy; Learning from observation and discovery; Learning by experimentation; Learning by training Neural Networks; Genetic Algorithm; Analysis learning; Reinforcement learning ;Applications to KDD. Unit-2 Lectures:12 Algorithmic models of learning. Learning classifiers, functions, relations, grammars, probabilistic models, value functions, behaviors and programs from experience. Bayesian, maximum a posteriori, and minimum description length frameworks. Parameter estimation, sufficient statistics, decision trees, neural networks, support vector machines, Bayesian networks, bag of words classifiers, N-gram models; Markov and Hidden Markov models, probabilistic relational models, association rules, nearest neighbor classifiers, locally weighted regression, ensemble classifiers. Unit-3 Lectures: 10 Computational learning theory, mistake bound analysis, sample complexity analysis, VC dimension, Occam learning, accuracy and confidence boosting. Dimensionality reduction, feature selection and visualization. Clustering, mixture models, k-means clustering, hierarchical clustering, distributional clustering. Reinforcement learning; Learning from heterogeneous, distributed, data and knowledge. Unit-4 Lectures: 8 Selected applications in data mining, automated knowledge acquisition, pattern recognition, program synthesis, text and language processing, internet-based information systems, human-computer interaction, semantic web, and bioinformatics and computational biology. References

1. Mitchell, Machine Learning, McGraw-Hill. 2. Marsland, Machine learning: an algorithmic perspective, CRC Press, Taylor and Francis

Group. 3. Bishop, C.:Pattern Recognition and Machine Learning. Berlin: Springer-Verlag. 4. Baldi, P. and Brunak, S. (2002): Bioinformatics: A Machine Learning Approach. Cambridge,

MA: MIT Press.

Annexure-I


PAPER CODE MST 226 PAPER NAME Modelling & Simulation CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Introduction to modelling and simulation. Definition of System, classification of systems, classification and limitations of mathematical models and its relation to simulation. Unit-2 Lectures: 08 Methodology of model building Modelling through differential equation: linear growth and decay models, nonlinear growth and decay models, Compartment models. Unit-3 Lectures: 12 Checking model validity, verification of models, Stability analysis, Basic model relevant to population dynamics, Ecology, Environment Biology through ordinary differential equation, Partial differential equation and Differential equations. Unit-4 Lectures: 10 Basic concepts of simulation languages, overview of numerical methods used for continuous simulation, Stochastic models, Monte Carlo methods. References

1. D. N. P. Murthy, N. W. Page and E. Y. Rodin, Mathematical Modeling, Pergamon Press. 2. J. N. Kapoor, Mathematical Modeling, Wiley Estern Ltd. 3. P. Fishwick: Simulation Model Design and Execution, PHI, 1995, ISBN 0-13-098609-7 4. M. Law, W. D. Kelton: Simulation Modeling and Analysis, McGraw-Hill, 1991, ISBN 0-07-

100803-9. 5. J. A. Payne, Introduction to Simulation, Programming Techniques and Methods of Analysis,

Tata McGraw Hill Publishing Co. Ltd. 6. F. Charlton, Ordinary Differential and Differential equation, Van Nostarnd.

Annexure-I


PAPER CODE MST 227 PAPER NAME Mathematical Software and Tools CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 MATLAB: Basic Introduction: Simple arithmetic calculations, Creating and working with arrays, numbers and matrices. Unit-2 Lectures:8 Creating and printing simple plots, Function files, Applications to Ordinary differential equations: A first order ODE, A second order ODE, ode23, ode45, Basic 2-D plots and 3-D plots. Unit-3 Lectures: 12 Mathematica: Basic introduction: Arithmetic operations, functions, Graphics: 2-D plots, 3-D plots, Plotting the graphs of different functions, Matrix operations, Finding roots of an equation, Finding roots of a system of equations, Solving differential equations. Unit-4 Lectures: 15 Basic Introduction: Mathematical symbols and commands, Arrays, Formulas, and Equations, Spacing, Borders and Colors, Using date and time option in LaTeX, To create applications and Letters, PPT in LaTeX, Writing an article, Pictures and Graphics in LaTeX. References

1. R. Pratap: Getting started with MATLAB, Oxford University Press, 2010. 2. S. Lynch, Dynamical Systems with Applications using MATLAB, Birkhäuser, 2014. 3. M. L. Abell, J.P. Braselton, Differential Equations with Mathematica, Elsevier Academic

Press, 2004. 4. P. Stavroulakis, S.A. Tersian, An Introduction with Mathematica and MAPLE, World

Scientific, 2004. 5. L.W. Lamport, LaTeX: A document Preparation Systems, Addison-Wesley Publishing

Company, 1994. 6. H. Kopka, P.W. Daly, Guide to LATEX, Fourth Edition, Addison Wesley, 2004

Annexure-I


PAPER CODE MST 301 PAPER NAME Decision Theory & Non Parametric Inference CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 Basic elements of Statistical Decision Problem. Expected loss, decision rules (nonrandomized and randomized), decision principles (conditional Bayes, frequentist), inference as decision problem, optimal decision rules. Bayes and minimax decision rule. Admissibility of minimax rules and Bayes rules. Unit-2 Lectures: 15 Subjective probability, Prior distribution, subjective determination of prior distribution. Improper priors, non-informative (default) priors, invariant priors. Conjugate prior families, hierarchical priors and Parametric Empirical Bayes. Posterior distribution, Loss function, squared error loss, precautionary loss, LINEX loss. Bayes HPD confidence intervals. Unit-3 Lectures: 10 Definition and construction of S.P.R.T. Fundamental relation among A and B. Wald’s inequality. Determination of A and B in practice. Average sample number and operating characteristic curve Unit-4 Lectures: 10 Nonparametric and distribution-free tests, one sample problems and problem of symmetry, Sign test, Wilcoxon signed rank test, Kolmogorov-Smirnov test. Test of randomness using run test. General two sample problems: Wolfowitz runs test, Kolmogorov Smirnov two sample test (for sample of equal size), Median test, Wilcoxon-Mann-Whitney U-test References

1. Berger, J.O.: Statistical Decision Theory and Bayesian Analysis, 2nd Edition. Springer Verlag.

2. Bernando, J.M. and Smith, A.F.M. Bayesian Theory, John Wiley and Sons. 3. Robert, C.P.: The Bayesian Choice: A Decision Theoretic Motivation, Springer. 4. Ferguson, T.S.: Mathematical Statistics – A Decision Theoretic Approach, Academic Pres.

5. George Casella, Roger L. Berger: Statistical Inference, 2nd ed., Thomson Learning. 6. Rohatagi, V.K.: An Introduction to Probability and Mathematical Statistics, Wiley Eastern,

New Delhi. 7. Rao, C.R. Linear Statistical Inference and its Applications, Wiley Eastern.

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PAPER CODE MST 302 PAPER NAME Time Series Analysis & Forecasting CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Basics of Time series: A model Building strategy, Time series and Stochastic process, stationarity, Auto correlation, meaning and definition–causes of auto correlation-consequence of autocorrelation–test for auto–correlation. Study of Time Series model and their properties using correlogram, ACF and PACF. Yule walker equations Unit-2 Lectures:10 Time Series Models: White noise Process, Random walk, MA, AR, ARMA and ARIMA models, Box- Jenkins’s Methodology fitting of AR(1), AR(2), MA(1), MA(2) and ARIMA(1,1) process. Unit root hypothesis, Co-integration, Dicky Fuller test unit root test, augmented Dickey – Fuller test. Unit-3 Lectures: 10 Non-linear time series models, ARCH and GARCH Process, order identification, estimation and diagnostic tests and forecasting. Study of ARCH (1) properties. GARCH (Conception only) process for modelling volatility. Unit-4 Lectures: 10 Multivariate Liner Time series: Introduction, Cross covariance and correlation matrices, testing of zero cross correlation and model representation. Basic idea of Stationary vector Autoregressive Time Series with orders one: Model Structure, Granger Causality, stationarity condition, Estimation, Model checking. References

1. Box, G. E. P. and Jenkins, G. M.: Time Series Analysis – Forecasting and Control, Holden – day, San Francisco.

2. Chatfield, C. : Analysis of Time Series, An Introduction, CRC Press. 3. Ruey S. Tsay :Analysis of Financial Time Series, Second Ed. Wiley& Sons. 4. Ruey S. Tsay :Multivariate Time series Analysis: with R and Financial Application, Wiley&

Sons. 5. Montgeomery, D. C. and Johnson, L. A.:Forecasting and Time series Analysis, McGraw Hill. 6. Kendall, M. G. and Ord, J. K. :Time Series ( Third edition), Edward Arnold. 7. Brockwell, P. J. and Davies, R. A. :Introduction to Time Series and Forecasting( second

Edition – Indian Print). Springer. 8. Chatfield, C. :The Analysis of Time series: Theory and Practice. Fifth Ed. Chapman and Hall. 9. Hamilton Time Series Analysis 10. Jonathan, D. C. and Kung, S.C. :Time Series Analysis with R. Second Ed. Springer.

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PAPER CODE MST 303 PAPER NAME Multivariate Analysis CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Review of Multivariate Normal Distribution (MVND) and related distributional results. Random sampling from MVND, Unbiased and maximum likelihood estimators of parameters of MVND, their sampling distributions, independence. Correlation matrix and its MLE. Partial and multiple correlation coefficients, their maximum likelihood estimators (MLE) Unit-2 Lectures:10 Wishart distribution and its properties (only statement).Hotelling's T2 and its applications. Hotelling's T2statistic as a generalization of square of Student's statistic. Distance between two populations, Mahalnobis D2 statistic and its relation with Hotelling's T2 statistic. Unit-3 Lectures: 10

Classification problem, discriminant analysis. Principle component analysis. Canonical correlation.

Unit-4 Lectures: 10 Factor Analysis. Cluster Analysis

References 1. Kshirsagar A. M. : Multivariate Analysis. Maral-Dekker. 2. Johnosn, R.A. and Wichern. D.W.:Applied multivariate Analysis. 5thAd.Prentice –Hall. 3. Anderson T. W.: An introduction to Multivariate statistical Analysis2nd Ed. John Wiely. 4. Morrison D.F.: Multivariate Statistical Methods McGraw-Hill.

Annexure-I


PAPER CODE MST 306 PAPER NAME Practicals CREDIT 04 (0-0-4) TOTAL HOURS 45 CONTENT Students will be required to do practicals, based on topics listed below, using R software:

1. Plotting of time series data. 2. Plots of ACF and PACF 3. Fitting AR (p) and MA (q) models and Forecasting. 4. Residual analysis and diagnostic checking. 5. OLS estimation and prediction in GLM. 6. Trends and seasonality analysis. 7. Test for auto correlation. 8. ARCH and GARCH Models 9. Problem on test of symmetry and randomness 10. Problem on goodness-of-fit test 11. Plotting Posterior density and loss functions 12. Sampling from normal distributions, manzinal and conditional distributions 13. Testing for mean and variance 14. Application of Hotellings T2 statistic 15. Principle component 16. Discrimination and classification problems 17. Canonical correlations

There shall be minimum two practical assignments from each elective course.

Annexure-I


PAPER CODE MST 321 PAPER NAME Statistical Quality Control CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 General theory and review of control chart for attributes and variables, OC and ARL of control chart, Statistical process control short production runs, Modified and acceptance control charts. Unit-2 Lectures:10 Statistical process control with auto-correlated process data, Adaptive sampling procedures, Economic design of control chart, Cuscore charts, Control charts in health care monitoring and Public health surveillance. Unit-3 Lectures: 15 Producer’s risk, Consumer’s risk, Acceptance sampling plan, Single and double sampling plans by attributes, OC, ASN (and ATI), LTPD, AOQ and AOQL curves, Single sampling plan for variables (one sided specification, known and unknown cases), use of IS plans and tables. Unit-4 Lectures: 10 Multiple sampling plans, Sequential sampling plan, The Dodge-Roaming sampling plan, Designing a variables sampling plan with a specified OC curve, Other variables sampling procedures. Continuous sampling References

1. D.C. Montgomery: Introduction to Statistical Quality Control. Wiley. 2. Wetherill, G.B. Brown, D.W.: Statistical Process Control Theory and Practice, Chapman &

Hall. 3. Wetherill, G.B.: Sampling Inspection and Quality control, Halsteed Press. 4. Duncan A.J.: Quality Control and Industrial Statistics, IV Edision, Taraporewala and Sons. 5. Ott, E. R. : Process Quality Control (McGraw Hill)

Annexure-I


PAPER CODE MST 322 PAPER NAME Stochastic Finance CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Mechanism of Options markets, Types of Options, Option positions, Derivatives, Underlying Assets, Specification of stock options, Stock option pricing, Factors affecting option prices, Upper and lower bounds for option prices, Trading strategies involving options, Binomial model: One-step and two-step models, Binomial trees. Risk neutral valuation. Unit-2 Lectures: 10 Brownian Motion, Weiner Process, Quadratic Variation, Arithmetic and Geometric Brownian motion, Review of basic properties and related martingales, Applications to insurance problems, Ito Lemma, Ito integral, Applying Ito Lemma. Unit-3 Lectures: 10 Black-Scholes model: Distribution of rate of returns, volatility, risk neutral pricing, Discrete and Continuous Martingale pricing, Idea underlying the Black-Scholes-Merton differential equation, Estimating volatility Unit-4 Lectures: 10 Greek Letters and hedging, Interest rate derivatives, Black model References

1. Hull John C. and Basu S. (2010) Options, Futures and Other derivatives, 3rd Prentice hall of India Private Ltd., New Delhi.

2. Sheldon M Ross (2005): An elementary Introduction to Mathematical Finance, Cambridge University Press.

3. Joshi M.S. (2010): The Concept and Practice of Mathematical Finance, Cambridge University Press.

4. Shreve Steven E.(2009) Stochastic Calculus for Finance I: The Binomial Asset Pricing models, Springer.

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PAPER CODE MST 323 PAPER NAME Contingencies CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 The future lifetime random variable–complete ( xT ), curtate ( xK ) and 1/mthly ( ( )m

xK ). Survival and

mortality probabilities and functions, including , , , ( )t x t x t u x xp q q t and select versions. Life tables and their uses; the life table functions for select and ultimate lives. UDD and constant force of mortality fractional age assumptions. Unit-2 Lectures:12 Definitions, distributions, calculations of probabilities and moments for insurance benefit present value random variables, including standard international actuarial notation. Definitions, distributions, calculations of probabilities and moments for annuity present value random variables, including standard international actuarial notation. Unit-3 Lectures: 10 The future loss random variable for insurance contracts, The equivalence principle for net and gross premium calculation, Calculation of prospective reserves using the future loss random variable, Recursions for reserves, Thiele’s equation: solving the ODE. Unit-4 Lectures: 8 Multivariate random variables, Joint life status, Last survivor status, Joint survival functions, Common shock model, Insurance for multi--life models, Deterministic survivorship group, Random survivorship group, Stochastic model for multiple decrements References

1. David C. M. Dickson, Mary R. Hardy, Howard R. Waters (2009) Actuarial Mathematics for Life Contingent Risks, Cambridge University Press.

2. Shailja R Deshmukh: Actuarial Statistics using R, University Press. 3. Booth, P.M et al.:Modern Actuarial Theory and Practice, Chapman & Hall. 4. Gerber, H.U.: Life Insurance Mathematics,3rd ed. Springer, Swiss Association of Actuaries 5. Browers Newton L et al..:Actuarial Mathematics (2nd ed.) Society of Actuaries

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PAPER CODE MST 324 PAPER NAME Principles & Practice Of Insurance CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Origin, Development and Present Status of Insurance, Risk Management, List out the Benefit and Cost of Insurance, Fundamental Key Principles of Insurance, Types of Insurance Contracts, Classification of Insurance. Unit-2 Lectures:10 Classification of insurance in life and non-life insurance, micro insurance, social insurance and general insurance (motor, marine, fire, miscellaneous), Types of insurance plans: whole life, term, endowment. Unit-3 Lectures: 10 Types of investments and saving, Insurance, Shares, Bonds, Annuities, Mutual and Pension Fund. Unit-4 Lectures: 10 Basics of Under-writing, Claims Management, Reinsurance, Legal and Regulatory Aspects of Insurance. Seminar/Assignments: Each student will have to prepare his/ her presentation/ making assignments based on any topic from Actuarial Science and presents it. The topics will cover cases studies covering various aspects of the principles of insurance including IRDA regulations, publications, the 1938 Act 2006 and accounting standards. References

1. Principles and Practice if Life Insurance, ICAI, New Delhi 2. Black & Skipper: Life and Health Insurance, Pearson Education 3. Harrington, Scott E. & Gregory R. : Risk Management and Insurance: 2nd ed., Tata Mc Graw

Hill Publicating Company Ltd. New Delhi

Annexure-I


PAPER CODE MST 325 PAPER NAME Data Mining CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Introduction to data mining & knowledge discovery in databases, Data mining v/s Databases, Complexities of Data mining, Application & future scope of data mining, the knowledge discovery process: normalization, converting, smoothing data, method for attribute elimination and creation. Unit-2 Lectures:10 Data mining versus KDD, Data mining versus OLTP, introduction to data warehouse, OLAP, Application areas of data mining, Functionality of Data mining. Unit-3 Lectures: 10 Data mining techniques: Simple data mining techniques & strategies, Association rule mining in large database: mining single dimensional Boolean association rules from transactional database. Apriori Algorithm, Mining multilevel association rules, constraint based association mining. Unit-4 Lectures: 10 Classification & Prediction: Introduction, issues regarding clustering and prediction, classification by K- nearest neighbours, decision tree: ID3, Introduction to Cluster Analysis: k- means clustering, nearest neighbouring clustering. Neural Networks, Introduction to web mining, Case study: Biomedical, Financial, Retail industry, web based. References

1. Data Mining–concepts & techniques by Jia wei han & Micheline kamber, Morgan Kaufman, published an imprint of Elsevier.

2. Data mining A tutorial based primer. By Richard J. Roiger, Michael W. Geatz, Pearson Education.3. Data Mining Introductory and Advanced topics. By Margaret H. Dunham. Pearson Education. 4. Data mining and data warehousing byTeck June Ho, Pearson/Prentice Hall, 2005 5. Data Mining By Gopalan & Sivaselvan, PHI Learning Pvt. Ltd. 6. Data mining: Theory, Methodology, Techniques and Applications By Graham J. Williams, Simeon

J. Simoff. Springer Science & Business, 2006 7. Data Mining Techniques by Arun K Punjari , University Press, 2007

Annexure-I


PAPER CODE MST 401 PAPER NAME National Development Statistics CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Economic development: Growth in per capital income and distributive justice, Indices of development, Human Development index, quality of life. Estimation of national income-product approach, income approach and expenditure approach. Unit-2 Lectures: 10 Population growth in developing and developed countries, Population projection using Leslie matrix, Labour force projection Unit-3 Lectures: 10

Poverty measurement-different issues, measures of incidence and intensity, combined measures e.q. indices due to Kakwani, Sen etc.

Unit-4 Lectures: 10

Statistical System of India: NSSO, CSO, NSSTA, MOSPI, NITI Ayoge, Different Institutions and committees are responsible for planning and execution of National Building.

References 1. Chatterjee, S.K.: Quality of life. 2. Chaubey, P. K.: Poverty Analysis, New Age International (P) Limited, Publishers. New Delhi. 3. Human Development Annual Report. 4. Sen, Amartya.: Poverty and Famines, Oxford University Press. 5. CSO. National Accounts Statistics- Sources and Health. 6. UNESCO: Principles of Vital Statistics Systems.

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PAPER CODE MST 406 PAPER NAME Practicals CREDIT 04 (0-0-4) Total hours 45 CONTENT There shall be minimum four practical assignments from each optional course. In case, there are the possibility to not get sufficient number of practical problems then there will be minimum one case study based each paper. Practical assignments/ case studies will be given by subject teacher.

Annexure-I


PAPER CODE MST 410 PAPER NAME Project CREDIT 08 DURATION 6 Weeks Guidelines for project Project duration: Students may start preliminary work related to their project after second

semester).

Project Guide: Teachers from the Department of Statistics and/or organization where student is

going to visit for field work or training. Each project group will be guided by concerned teacher

(guide) for one hour per week throughout the IV semester.

Project Topic: Students in consultation with the guide will decide project topic. The modification

on the title may be permitted after the pre-presentation as advised during the seminar in

consultation with the supervisor. Project work may be carried out in a group of students

depending upon the depth of fieldwork/problem involved.

Project report: Project report should be submitted in typed form with binding within the time as

stipulated be the Department.

Project evaluation: Project evaluation will be based on

(i) Continuous evaluation of the work – 25 Marks awarded by supervisor

(ii) Project report and final presentation - 25 marks awarded by supervisor

(iii) Viva-voce and final presentation - 50 marks awarded by external expert

Annexure-I


PAPER CODE MST 421 PAPER NAME Survival Models & Analysis CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Survival Characteristics and Parametric Models: Survival function, quantiles, hazard rate, cumulative hazard function, and mean residual life, Parametric models for study of event time data: Exponential, Weibull, extreme value, gamma, Pareto, logistic, log-logistic, normal, log–normal and mixture models -their survival characteristics. Parametric Inference: Longitudinal studies. Censoring mechanisms- type I, type II and left right and interval censoring. Likelihood function under censoring. Fitting parametric models to survival data with right censoring. Large sample tests with censored data. The E–M algorithm. Unit-2 Lectures:10 Nonparametric Inference: Actuarial and Kaplan–Meier estimators. Treatment of ties. Self-consistency property and asymptotic properties of K–M estimator (statement). Pointwise confidence interval for S(t). Nelson-Aalen estimator of cumulative hazard function and estimation of S(t) based on it. Two–sample methods. Comparison of survival functions: Log rank and Tarone-Ware tests. Competing risks model; Kaplan-Meier estimator of survival function, Nelson-Aalen estimator. Unit-3 Lectures: 10 Semi-parametric Inference: Explanatory variables- factors and variates. Cox proportional hazards model. The partial likelihood and estimation of regression coefficients and their standard errors. Breslow’s estimator of the baseline hazard function; estimation of cumulative hazard rate and S(t). Statement of asymptotic properties of the estimator. Confidence interval for regression coefficients. Wald, Rao and likelihood tests for β. Accelerated life model. Model selection criteria and comparison of nested models (-2logL and AIC). Using information on prognostic variables in a competing risks model. Unit-4 Lectures: 10 Parametric regression-Weibull and Gompertz models. Residuals and model checking under Cox and parametric models. Comparing two survival curves. Hazard plots, Survival plots. Comparing alternative models, AIC criterion. Comparing observed and fitted survival models. Testing proportional hazards hypothesis in the Weibull model of cumulative incidence function. References

1. Klien, J.P. and Moeschberger, M.L.:. Survival Analysis: Techniques for censored and Truncated Data. 2/e. Springer.

2. Kalbfleisch, J.D. and Prentice, R. L.:, The Statistical Analysis of Failure Time Data, 2nd edition, J. Wiley, New York.

3. Collett, D.:. Modelling Survival Data in Medical research. 2/e. Chapman & Hall. 4. Lawless, J. F:, Statistical Models and Methods for Lifetime Data, J. Wiley, New York. 5. Nelson, W: Applied Life Data Analysis, J. Wiley, New York. 6. Miller, J: Survival Analysis, J. Wiley, New York. 7. Elandt-Johnson, Regina C; Johnson, Norman L:Survival models and data analysis. Classics

Library ed. – John Wiley & Sons.

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PAPER CODE MST 422 PAPER NAME Advance Bayesian Inference CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Need of Bayes estimation. Advantage of Bayesian inference, Prior distribution, Posterior distribution, Subjective probability and its uses for determination of prior distribution. Importance of non-informative priors, improper priors, invariant priors. Conjugate priors, construction of conjugate families using sufficient statistics, hierarchical priors, Parametric Empirical Bayes. Unit-2 Lectures: 20 Point estimation, Concept of Loss functions, Bayes estimation under symmetric and asymmetric loss functions, Bayes credible intervals, highest posterior density intervals, testing of hypotheses. Comparison with classical procedures. Ideas on Bayesian robustness. Predictive inference. One- and two-sample predictive problems. Posterior predictive for ordered observations from exponential and other distributions. Unit-3 Lectures: 10 Bayesian calculation, Lindley’s approximation, T-K approximation, Monte-Carlo Integration, Markov chain Monte Carlo techniques. References

1. Berger, J. O. : Statistical Decision Theory and Bayesian Analysis, Springer Verlag. 2. Robert, C.P. and Casella, G. : Monte Carlo Statistical Methods, Springer Verlag. 3. Leonard, T. and Hsu, J.S.J. : Bayesian Methods, Cambridge University Press. 4. Bernando, J.M. and Smith, A.F.M. : Bayesian Theory, John Wiley and Sons. 5. Robert, C.P. : The Bayesian Choice: A Decision Theoretic Motivation, Springer. 6. Gemerman, D. : Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference,

Chapman Hall. 7. Box, G.P. and Tiao, G. C.: Bayesian Inference in Statistical Analysis, Addison-Wesley.

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PAPER CODE MST 423 PAPER NAME Statistical Quality Management CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 Moving average and exponentially weighted moving average charts, Cu-sum charts using V-masks and decision intervals. Economic design of തܺ–chart. Multivariate control charts. Unit-2 Lectures:10 Acceptance sampling plans for inspection by variables for two sided specifications. Millitary Standard 105E (ANSI/ASQC Z1.4, ISO 2859) plans. Unit-3 Lectures: 10 Continuous Sampling plans of Dodge type and Wald-Wolfowitz type and their properties, Bulk and chain sampling plans, Bayesian sampling plans. Role of statistical techniques in quality management. Unit-4 Lectures: 15 Process Capability Indices:ܥ ܥ, ܥ , ܥ , estimation, confidence intervals and test of hypotheses for normally distributed characteristics. Process capability analysis using control chart, Process capability analysis with attribute data. Gauge and Measurement System capability studies. References

1. D.C. Montgomery: Introduction to Statistical Quality Control. Wiley. 2. Wetherill, G.B. Brown, D.W.: Statistical Process Control Theory and Practice, Chapman

& Hall. 3. Wetherill, G.B.: Sampling Inspection and Quality control, Halsteed Press. 4. Duncan A.J.: Quality Control and Industrial Statistics, IV Edision, Taraporewala and Sons. 5. Ott, E. R.: Process Quality Control (McGraw Hill)

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PAPER CODE MST 424 PAPER NAME Statistical Methods for Non-Life Insurance CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Review of Loss distributions: Classical loss distributions, heavy-tailed distributions, reinsurance and loss distributions. Reinsurance and effect of inflation. Unit-2 Lectures:10 Risk models for aggregate claims: Collective risk model and individual risk model, premiums and reserves for aggregate claims, reinsurance for aggregate claims. Unit-3 Lectures: 10 Ruin theory: Surplus process in discrete time and continuous time, probability of ruin in finite and infinite time, adjustment coefficient, Lundberg inequality, applications in reinsurance. Unit-4 Lectures: 10 Introduction to Bayesian inference, Credibility Theory, Full credibility for claim frequency, claim severity and aggregate loss. Bayesian credibility, Empirical Bayes credibility. References

1. Boland P.J.: Statistical and probabilistic Methods in Actuarial Science. Chapman & Hall, London.

2. Bowers, JR. N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J.: Actuarial Mathematics, Second Edition, The Society of Actuaries. Sahaumburg, Illinois.

3. Dickson, D.C. M.: Insurance Risk and Ruin, Cambridge University Press, Cambridge. 4. Grandell, J. :Aspects of Risk theory, Springer-Verlag, New York 5. Mikosch, T.: Non-Life Insurance Mathematics, Springer, Berlin. 6. Ramasubramanian, S. :Lectures on Insurance Models, Hindustan Book Agency Texts and

Readings in Mathematics (trim).

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PAPER CODE MST 425 PAPER NAME Life & Health Insurance CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 10 Introduction to life and health insurance, various types of life and health insurance plans, available insurance policies in the Indian market Unit-2 Lectures:10 Conventional non-participating life insurance, Linked accumulating non-participating contracts , Non-linked Accumulating Non-participating Contracts Participating Life Insurance, Different Distribution Methods, Profit Distribution Strategies, With-profit polices, Dividends and Bonus Method Unit-3 Lectures: 10 Health insurance data, pricing & reserving, Classification of group and individual insurance plan under life and health insurance, Social security schemes, Method of valuation, Analysis of surplus Unit-4 Lectures: 15 The actuarial role in life office management: Introduction, product pricing, analysis of surplus, monitoring and uploading the assumptions in the control cycle. Further uses of models in Actuarial management. Students are also expected to complete three assignments: i. Each student is expected to write a brief report on an appropriate/ relevant real life problem

related to life insurance/health insurance/ general insurance using statistical tools and techniques. ii. Review one insurance existing policy in Indian market and advise change with comparative

analysis. iii. Review some case study reported to different insurance companies administrative or legal

authorities of the University. References

1. Black & Skipper: Life and health insurance, Pearson Education 2. Philip Booth et al.: Modern actuarial theory and practice, Second edition, Chapman and

Hall/CRC

Annexure-I


PAPER CODE MSTA 426 PAPER NAME Employee Benefit Plans CREDIT 04(3-1-0) Total hours 45 Unit-1 Lectures: 10 Leave Encashment, Leave availment, Gratuity, Service awards, Pension, Post-Retirement Medical Scheme, Demographic Consideration-Mortality, attribution rates, Economic Consideration: Salary rise, Discounting rate, Reconciliation of Liability over IVP, Reconciliation of Asset over IVP, Valuation Methods, Contribution rates, Fund flow, Current service cost, Actuarial Gain/loss, Experience Adjustments, Balance sheet and PL A/c figures. Unit-2 Lectures:10 Leave Encashment: Annual Leave (P/S/C), Maximum Accrual, Minimum balance, limit of various kinds, Encashment Rules, Leave Availment, Availment/Encashment, LIFO, Unit-3 Lectures: 10 Gratuity: Qualifying Period, Qualifying Salary for PoG, Limits on gratuity, Service Awards: Progressive Service Awards, Long terms service awards, Other benefits-daughter’s marriage Unit-4 Lectures: 15 Pension: Who are covered? (Self/spouse/children), Formula for Pension- related to terminal salary and Length of service(LOS), Qualifying LOS, Pension amount- Fixed or enhancement allowed on account of compensation for inflation, Re-installment of full pension, Post Retirement, Medical Scheme: Who is covered-self/spouse, OPD, ID, severe disease. References

1. Accounting Standard (AS) 15- Revised Benefits- Employee Benefits

Annexure-I


PAPER CODE MSTA 427 PAPER NAME Valuation and Loss Reserving CREDIT 04(3-1-0) Total hours 45 Unit-1 Lectures: 15 Basic Concept: The Claim Process, Estimating Outstanding Loss Liability, Loss Reserving, Illustrations, Claim Counts: Exposure, IBNR Claims, Claim frequency, Other models. Unit-2 Lectures:10 Claim amount- Simple Models- Case Estimation, chain ladder, Separation Methods, Claim amount: Other Models like Payment Based Models, Claim Closure based Models, Case Estimates based models. Unit-3 & 4 Lectures: 20 Minor Project and Seminar Presentations: Each student is expected to write a brief reporting (in the form of Minor project) on an appropriate/relevant real life problem related to ―Life Insurance, Health insurance, General Insurance‖ or may be any relevant topics in Insurance using statistical tools and techniques. It is also expected to give seminar on the project. References

1. Greg Taylor, Loss Reserving, An Actuarial Perspective, Kluwer Academic Publishers. 2. Lecture Notes on Loss Reserving with Random Selection.

Annexure-I


PAPER CODE MST 228 PAPER NAME Finance & Financial Reporting CREDIT 04(3-1-0) TOTAL HOURS 45 Unit-1 Lectures: 15 Key principles of Finance; principal terms in use for investment and asset management, Profit maximization and wealth maximization, Basic principles of personal and corporate taxation, Major types of financial institution operating in the financial markets. Unit-2 Lectures:10 Definition of company’s cost of capital; weighted average cost of capital, Capital Structure: factors to be considered by a company when deciding on its capital structure, capital structure theories, optimum capital structure, Dividend policy and valuation of a firm. Unit-3 Lectures: 10 Assessment of capital investment projects: DCF and non-DCF techniques, Structure of a joint stock company and different methods by which it may be financed. Unit-4 Lectures: 10 Basic construction of accounts of different types and the role and principal features of the accounts of a company, Interpretation of the accounts of a company. Ratio Analysis; fund flow and cash flow analyses; limitations of the interpretations. References

1. Institute of actuaries core reading material for CT -2 Finance and Financial Reporting 2. Financial statement analysis in Europe. - Samuels, J M; Brayshaw, R E; Craner, J M. -

Chapman & Hall, 1995. 454 pages - ISBN: 0 412 54450 4. 3. Fundamentals of financial management. - Brigham, Eugene F; Houston, Joel F. - 9th ed. -

Harcourt Brace, 2000. 959 pages - ISBN: 0 03 031461 5. 4. How to read the financial pages. - Brett, M. 2nd ed. Random House Business Books, 2003.

430 pages. ISBN: 0712662596. 5. Interpreting Company Reports and Accounts. - Holmes, Geoffrey; Sugden, Alan;Gee, Paul. -

8th ed. - Pearson Education, 2002. 298 pages - ISBN: 0 273 65592 2. 6. Principles of Corporate Finance. - Brealey, Richard A; Myers, Stewart C. - 7th ed. -McGraw-

Hill, 2003. 1004 + appendices pages - ISBN: 0 07 115144 3.

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