f(x;0,B) = {{z+B)Q+T Question 9. Let X be a random variable having density given by if r > 0 elsewhere where a > 0 and 8 >0 are parameters. (a) (5 pts) If a > 0, show that B E[X] = Q- -1 (b) (5 pts) Let k E N such that a > k. If X has pdf f(x; a,B) and Y has pdf f(y;a 1,8), where f is as above, show that Bk E [**] => (c) (5 pts) Deduce a general formula for E (Xk] when a > k. f(x;0,B) = {{z+B)Q+T Question 9. Let X be a random variable having density given by if r > 0 elsewhere where a > 0 and 8 >0 are parameters. (a) (5 pts) If a > 0, show that B E[X] = Q- -1 (b) (5 pts) Let k E N such that a > k. If X has pdf f(x; a,B) and Y has pdf f(y;a 1,8), where f is as above, show that Bk E [**] => (c) (5 pts) Deduce a general formula for E (Xk] when a > k