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lectures, Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in 4-x 2 fx(x) = |x| 2. (a) Explain

 

lectures, Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in 4-x 2 fx(x) = |x| 2. (a) Explain why EX" = 0 for any positive odd integer n. Hint: use properties of odd functions. How about EX-? Is that also zero? Why or why not? (b) (c) Find E[Z], E[X], E[|Z|] and E[X]. (d) Explain why E[Ze2/2] is not zero even though h(z) = ze/2 is an odd function.

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