Question: Please help solve the following MATHEMATICAL STATISTICS problem: Problem 2 Suppose that Z ~ N(0, 1), and X has the Wigner semicircle distribution as specified

Please help solve the following MATHEMATICAL STATISTICS problem:

Problem 2 Suppose that Z ~ N(0, 1), and X has the Wigner semicircle distribution as specified in lectures, V4 -x2 fx ( x) = |x| 52. 2pts (a) Explain why EX" = 0 for any positive odd integer n. Hint: use properties of even functions. 1 pts (b) How about EX -1? Is that also zero? Why or why not? 8pts (c) Find E[IZ|], E[IX|], E[IZ |3] and E[| X | 3]. 1 pts (d) Explain why E[ZeZ /2] is not zero even though h(z) = zez /2 is an even function

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