Find EYm Using the result from a show that the mean of Y is

Find E(Y^m)

Using the result from a) show that the mean of Y is

Find the variance of Y

Solution

Given Y~gamma(lambda,alpha) ,so M_Y(t)=[1/(1-(t/lambda))]^alpha, so K_y(t)=alpha[(t/lambda)+((1/2)*(t/lambda)²)+((1/3)*(t/lambda)³)+........]. Then mean=(alpha/lambda) and variance= (alpha/lambda²). If lambda=1, then mean=variance=alpha.