Problem 1 Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in lectures, √4x² 2 fx (x)

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Problem 1 Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in lectures, √4x² 2 fx (x)

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Problem 1 Suppose That Z N 0 1 And X Has The Wigner Semicircle Distribution As Specified In Lectures 4x 2 Fx X 1
Problem 1 Suppose That Z N 0 1 And X Has The Wigner Semicircle Distribution As Specified In Lectures 4x 2 Fx X 1 (95.08 KiB) Viewed 31 times
Problem 1 Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in lectures, √4x² 2 fx (x) = |x|≤ 2. 2л 2 pts (a) Explain why EX" = 0 for any positive odd integer n. Hint: use properties of odd functions. -1 1 pts (b) How about EX-¹? Is that also zero? Why or why not? 8pts (c) Find E[|Z|], E[|X|], E[|Z|³] and E[|X|³]. 1pts (d) Explain why E[ZeZ²/2] is not zero even though h(z) = ze²²/² is an odd function.
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