Suppose that Y has a gamma distribution with parameters α and β. a If a is any positive or negative value such that α + a > 0, show that E(Ya ) = βa(α + a) (α) . b Why did your answer in part (a) require that α + a > 0? c Show that, with a = 1, the result in part (a) gives E(Y ) = αβ. d Use the result in part (a) to give an expression for E( √Y ). What do you need to assume about α? 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 α in each case?
