7 nomrmal distrbuition (2)

7 nomrmal distrbuition (2) - Homework #2 Due September 26,...

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Due September 26, 2008 (Friday) 5:00PM Homework #2
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October 13, 2008 (Monday) Preliminary presentation for project
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October 20, 2008 (Monday) Mid-term exam
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MFG5350 4 Distribution Review
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MFG5350 5 Random Variables Random variables can be discrete or continuous If the random variable x assumes a finite number of values , then x is called a discrete random variable The time to failure of a component The number of failures occurring in some time t The time to repair a failed system The number of cycles until the first failure occurs (continuous) (continuous)
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MFG5350 6 Discrete Probability Distributions Binomial Distribution Poisson Distribution Geometric Distribution
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MFG5350 7 Binomial Distribution Applied to situations where an event is either occur or not occur (success or failure) Let the probability of success is p, the the probability of failure is 1-p . Let the total number of independent trials be n , and the number of successes be r . r n r p p r n r X P 1 ) ( E[X]=np Var[X]=np(1-p) X ~ B(n,p)
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MFG5350 8 Poisson Distribution The Poisson distribution is most commonly used to model the number of random occurrences of some phenomenon in a specified unit of space or time. ! ) ( x e x P x E[X]= Var[X]= X ~ Po( ) For example, • Number of accidents per month in a factory • Number of blemishes per shirt x=0,1,2…
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9 Geometric Distribution The Geometric random variable is the number of trials required to obtain the first success. For example, X could be the number of independent coin tosses required
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This note was uploaded on 04/25/2010 for the course IE 654 taught by Professor Smith during the Spring '10 term at 카이스트, 한국과학기술원.

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7 nomrmal distrbuition (2) - Homework #2 Due September 26,...

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