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Unformatted text preview: y t âˆ« âˆž= Î“ 1 ) ( = Î“ ) ( n Gamma distribution Î¸ Î± / 1 ) ( 1 ) ( x e x x fÎ“ = âˆž < â‰¤ x E[X]= Î±Î¸ Var[X]= 2 Example : Customers arrive at Staples according a Poisson distribution with mean rate 1/2 per minute. Staples opens on 9:00am in the morning. W]hat is the probability that the second customer arrives after 9:05am? Ping Ma Lecture 15 Fall 2005 2 Special case of Gamma distribution 2 , 2 r = = Î± Î¸ where r is a positive integer. / 1 ) ( 1 ) ( x e x x fÎ“ = 2 / 1 2 / 2 / 2 ) 2 / ( 1 x r r e x rÎ“ = Chisquare distribution with r degrees of freedom, ) ( 2 r Ï‡ E[X]= Î±Î¸ = r r = 2 2 Var[X]= 2 = r r 2 2 2 2 = 100(1) th percentile ) ( 2 r 100 th percentile ) ( 2 1 rPing Ma Lecture 15 Fall 2005 3 ...
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 Fall '05
 TBA
 Statistics, Normal Distribution, Poisson Distribution, Probability theory, Cumulative distribution function, Staples, mean rate, free flash drive

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