Please help with this question.

(4 points) Let Z ~ N(0, 1) be the standard normal distribution, and X ~ N(M, o2). (a) Prove that E[Z3] = 0 and E[Z*] = 3 by evaluating the following integrals: E[Z3] = 4(2)203 dx = 1 x 2 1 2 2 e 2 xdx and E[Z*] - 4(x)x*dx = e 2 x'dx. V2TT -0O V2TT Le 2 Here 4(x) = 12T 2 is the p.d.f. of Z. (Hint: note that e- 2 x = (-e-2 )', and try to integrate by parts.) (b) Calculate E(X4). (Hint: try to relate X with Z, and use the result from part (1) instead of calculating integrals.)