15 Poisson - The Poisson Distribution The Poisson...

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1/5/10 The Poisson Distribution The Poisson Distribution is another extremely important distribution in Probability and Statistics. It is especially important for Industrial Engineers for reasons that will become apparent. The distribution was discovered by Siméon-Denis Poisson (1781–1840)
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1/5/10 Relation to Binomial The Poisson distribution is derived from the Binomial by letting N¸ 1 and p&0 but all the time keeping Np=& constant. For example: N 10 100 1000 10,000 ----------------------------------------- ....... & = 1 always
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1/5/10 Mean and Variance The mean and variance of the Poisson can be shown (after a lot of tedious math) to be: E(X) = & and V(X) = 1 λ = = = - = - = = = = - = - - = - = - = - ) 1 ( ! ) ( ! ) 1 ( ! ) 1 ( ! ! ) ( 0 1 1 1 1 0 k k j j j j j j j j k e j e j e j je j je X E
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1/5/10 Example Suppose 100 chips are manufactured on a line which has historically produced 5% defective chips. What is
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This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.

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15 Poisson - The Poisson Distribution The Poisson...

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