Unformatted text preview: n ) that Y = X 1 + . . . + X n has the negative binomial distri-bution 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 pa-rameter λ i . Deﬁne Y = ∑ n i =1 X i . Compute E ( Y k ) for k = 1 , . . . , 4. (Doing this for n = 4 will be full credit.)...
View Full Document
This homework help was uploaded on 02/03/2008 for the course MATH MATH 180A taught by Professor Castro during the Fall '08 term at UCSD.
- Fall '08