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7 nomrmal distrbuition (2)

# 7 nomrmal distrbuition (2) - Homework#2 Due(Friday 5:00PM...

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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
October 20, 2008 (Monday) Mid-term exam

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MFG5350 4 Distribution Review
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
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…
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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7 nomrmal distrbuition (2) - Homework#2 Due(Friday 5:00PM...

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