34. A random variable X having density function f (x ) - de -1x ( 2x ) a -1 x > 0 [(a) is said to have gamma distribution with parameters a > 0, > > 0, where T(a) is the gamma function defined by r(a) = ex"-dx, a -Q (a) Show that the preceding is a density function. That is, show that it is nonnegative and integrates to 1. (b) Use integration by parts to show that [(a + 1) = ar(a) Show that I(n) = (n - 1)!,n > 1 Find E[ X ] . Find Var(X)