Suppose that Y has a gamma distribution with parameters and . a If a is any positive or
Chapter 4, Problem 4.111(choose chapter or problem)
Suppose that Y has a gamma distribution with parameters and . a If a is any positive or negative value such that + a > 0, show that E(Ya ) = a( + a) () . b Why did your answer in part (a) require that + a > 0? c Show that, with a = 1, the result in part (a) gives E(Y ) = . d Use the result in part (a) to give an expression for E( Y ). What do you need to assume about ? e Use the result in part (a) to give an expression for E(1/Y ), E(1/ Y ), and E(1/Y 2). What do you need to assume about in each case?
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