experiment method & data analysis presentation the center for high energy physics kyungpook...

Kyungpook National University

Hye Yoon Chin 1

Experiment Method & Data analysis PresentationThe Center For high Energy Physics

Error & DistributionExperiment Method and Data analysis pro. K.H Chostudent # : 2002219014Hye yoon Chin March 20th 2003


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• Error?1. Occurrence cause of error ( 오차의 발생 원인 )

2. Kind of error ( 오차의 종류 )

3. Analysis of standard error ( 표준 오차의 해석 )

4. Propagation of error ( 오차의 전파 )

• Distributions?1. Distribution in general

2. Distribution special quality

3. The Gaussian Probability Distribution Function

4. Definition of Gaussian distribution


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1. Occurrence cause of error ( 오차의 발생 원인 )① natural error ( 자연오차 )

Tape measure that nature error happens according to wind, temperature, humidity, refraction, gravity, magnetic field change, and makes of steel has change of various length according to temperature change.

② instrumental errors ( 기계오차 ) Machine error happens when happen and moves measure

ment equipment by when control measurement equipment and imperfection sex of construction etc.

③ personal errors ( 개인오차 ) Produce personal error through sight difference and private

mistakes in roestretcher in principle.


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2. Kind of error( 오차의 종류 )

① 정오차 (constant errors) Complying with mathematical laws and physical rule, that say cumulative error. Constant error can remove the cause and state because was accumulated changelessly. For example, steel tape measure make up of length of 100 ㎝ actuality 99.9 ㎝ .Then, constant error is occurred that 0.1 ㎝ is omitted every time.


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② 우연오차 (accidental errors)

Accidental errors removes error that occur by constant errors and a mistake, the occurrence cause is not correct and exclusion is impossible errors. Accidental errors handles exclusion according to method of least squares by probability rule because is impossible.This accidental error is included in all measurement processes and fluctuates each other, compensation errors that do, and call that is variable error as comparison about systematic error .


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3. Nature of observational errors ( 관측 오차의 성질 )

• Correct value does not exist if see error of observation value and truth value that all measurement values have error and is observed can not know.And, truth error has propensity that is existed by unknown quantity always.


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• Because do 1 meter tape measure 10 division into equal parts, peel 10 ㎝ if divide notch mark on a scale, but can read, 10 centimeter by 1 centimeter notch mark on a scale divide, and 1 centimeter if divide notch mark on a scale by 1 millimeter to millimeter possible.

Accuracy of observation depends on the limit of partition of surveyor's measurement, the ability of equipment and environment.

Therefore, we may approach true value when we use the developed modern measurement equipment.


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• Mistake in measurement is insufficient judgment and carelessness, and is happening by misjudgment and so on about problem, and big fruit is thing by atrocity and is not happened in continuous process of error.Big fruit is searched as systematic public prosecutor of all measurement works and part that is repeated in Oeeop is removed or can be removed all.


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1. Distribution in general

While range, it is used most one of series random variable.Being random variable such as probability distribution of stalk shape that is right and left symmetry form in average, this random variable do formality probability jargon royal meal and probability distribution of formality random variable is known as normal distribution .Also, normal distribution is dependedon average and standard deviation.And average is 0 and standard deviation refers to 1 person normal distribution as standard normal distribution


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A person who find formality probability model by first is Abraham De Moivre (1667 ~ 1754), he saved in 1733 as limit form of binomial distribution.

It was introduced as probability distribution about error of laws of nature measure by Karl Friedrich Gauss (1777 ~ 1855) thereafter.

For these reason, called that is the normal function of error of normal distribution Gauss distribution or error.

Had been applied by probability matrix or approximative probability matrix astronomy, physics etc.. in many fields by the next


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2. Distribution special quality

• Normal distribution has graph of probability density function of bell-shaped and is symmetry about average

• Normal distribution is symmetry distribution, relation forms with clause of (average = median = 최빈수 ?)

• Formality random variable (normal random variable) selects much average surrounding value.However, distant value does not select mostly from average more than triple of standard deviation to right and left.

• Normal distribution is depended perfectly on its average and standard deviation.That is, two different normal distribution that average and standard deviation are same can not exist.


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정규분포의 PDF(Probability Density Function)

정규분포의 CDF(Cumulative Distribution Function)

정규분포의 MGF(Moment Generating Function)

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Karl Friedrich Gauss 1777-1855

3. The Gaussian Probability Distribution Function

= mean of distribution (also at the same place as mode and median) 2 = variance of distribution y is a continuous variable (-∞y ∞

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The Gaussian probability distribution is perhaps the most used distribution in all of science. Sometimes it is called the “bell shaped curve” or normal distribution.Unlike the binomial and Poisson distribution, the Gaussian is a continuous distribution:


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Probability (P) of y being in the range [a, b] is given by an integral:

The integral for arbitrary a and b cannot be evaluated analytically.The value of the integral has to be looked up in a table (e.g. Appendixes A and B of Taylor).

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4. Definition of Gaussian distribution

When dealing with very large numbers of particles, it is convenient to deal with a continuous function to describe the probability distribution, rather than the binomial distribution. The Gaussian distribution is the function that approximates the binomial distribution for very large numbers.

experiment method & data analysis presentation the center for high energy physics kyungpook...

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