7/29/2019 aaoczc111kufyvjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjhgy

1/2

AAOC ZC111 (EC-2 Regular) Page 1 of 2

Birla Institute of Technology & Science, Pilani

Distance Learning Programmes Division

Second Semester 2008-2009

Comprehensive Examination

(EC-2 Regular)

Course No. : AAOC ZC111

Course Title : PROBABILITY & STATISTICS

Nature of Exam : Open Book

Weightage : 60%Duration : 3 Hours

Date of Exam : 04/04/2009 (FN)

Note:1. Please follow all theInstructions to Candidates given on the cover page of the answer book.2. All parts of a question should be answered consecutively. Each answer should start from a fresh page.3. Mobile phones and computers of any kind should not be used inside the examination hall.4. Use of any unfair means will result in severe disciplinary action.Q.1 Suppose that a laboratory test on blood sample yields one of two results, positive

or negative. It is found that 95% of people with a particular disease produce a

positive. But 2% of people without the disease will also produce a positive result.

Suppose that 1% of the population actually has the disease. What is the probability

that a person chosen at random from the population(a)will have positive result.(b)will have the disease, given that the persons blood yields a positive result?

[6 + 4 =10]

Q.2 It has been found that 80% of all printers used on home computers operatecorrectly at the time of installation. The rest require some adjustment. A particulardealer sells 10 units during a given month. Find the probability that at least nine of

the printers operate correctly upon installation. [5]

Q.3 If a continuous random variable has the probability density function2( 2)

;0 1( ) 5

0 ; . .

xx

f x

e w

+ <

7/29/2019 aaoczc111kufyvjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjhgy

2/2

AAOC ZC111 (EC-2 Regular) Page 2 of 2

AAOC ZC111 (EC-2 Regular) Second Semester 2008-2009 Page 2

Q.5 Let X1 and X2 have the following joint probability distributionX2

0 1 2 3

0 0.409 0.108 0.027 0.008

1 0.308 0.047 0.015 0.006

X1

2 0.045 0.012 0.011 0.004

(a)Find P(X1 1, X2 1).(b)Find the marginal pdf for X1.(c)Find the marginal pdf for X2.(d)Find E(X1+ X2). [3 + 3 + 3 + 3 = 12]

Q.6 Two random samples of size 8 and 10 are drawn from two normally distributedpopulations having variance 20 and 36 respectively. Find the probability that thevariance of the first sample is more than twice the variance of the second sample.

[4]

Q.7 The Edison Electric Institute has published figures on the annual number ofkilowatt hours expended by various home appliances. It is claimed that a vacuum

cleaner expends on average of 46 kilowatt hours per year. If a random sample of12 homes included in a planned study indicates that a vacuum cleaner expends on

average of 42 kilowatt hours per year with a standard deviation of 11.9 kilowatt

hours. Test the null hypothesis = 46 kilowatt hours against the alternativehypothesis < 46 kilowatt hours at the 0.01 level of significance. Assume that thepopulation distribution is normal. [8]

Q.8 The grades of a class of 5 students on a midterm report (x) and on the finalexamination (y) are as follows:

x 77 50 71 96 81

y 82 66 78 99 47

Write the normal equations using the method of least squares and hence estimates a

regression line. [7]

**********