Consider a random variable Y belonging to the exponential family of the form f (y; 0) = exp(a(y)b(0) + c(0) + d(y)) (1) (a) Derive the expressions for E(a(Y) ) and Var(a(Y)). (b) Suppose the random variable X has the Gamma distribution with a scale param- eter 0, which is the parameter of interest, and a known shape parameter o. Show that the distribution of X belongs to the exponential family of the form in (1). State clearly the corresponding expressions of a(x), b(0), c(0) and d(x). (c) Using the results from Part (a), find E(X) and Var(X), for the Gamma random variable X. (d) Using the R function rgamma (), check your findings