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Unformatted text preview: n ) that Y = X 1 + . . . + X n has the negative binomial distribution with parameters ( n, p ) when the X i s are independent, each with the geometric distribution with parameter p . Hint: use the following identity X k = r k r = + 1 r + 1 . 5. Let X 1 , . . . , X n be independent, with X i having the exponential distribution with parameter i . Dene Y = n i =1 X i . Compute E ( Y k ) for k = 1 , . . . , 4. (Doing this for n = 4 will be full credit.)...
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 Fall '08
 Castro
 Probability

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