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**Unformatted text preview: **y t ∫ ∞--= Γ 1 ) ( = Γ ) ( n Gamma distribution θ α / 1 ) ( 1 ) ( x e x x f--Γ = ∞ < ≤ x E[X]= αθ 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 = = α θ where r is a positive integer. / 1 ) ( 1 ) ( x e x x f--Γ = 2 / 1 2 / 2 / 2 ) 2 / ( 1 x r r e x r--Γ = Chi-square distribution with r degrees of freedom, ) ( 2 r χ E[X]= αθ = r r = 2 2 Var[X]= 2 = r r 2 2 2 2 = 100(1-) th percentile ) ( 2 r 100 th percentile ) ( 2 1 r-Ping Ma Lecture 15 Fall 2005- 3 -...

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