lectures, Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in...
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lectures, Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in √4-x² 2π fx(x) = |x| ≤ 2. (a) Explain why EX" = 0 for any positive odd integer n. Hint: use properties of odd functions. How about EX-¹? Is that also zero? Why or why not? (b) (c) Find E[Z], E[X], E[|Z|³] and E[X³]. (d) Explain why E[Ze2²/2] is not zero even though h(z) = ze²²/2 is an odd function. lectures, Suppose that Z~ N(0, 1), and X has the Wigner semicircle distribution as specified in √4-x² 2π fx(x) = |x| ≤ 2. (a) Explain why EX" = 0 for any positive odd integer n. Hint: use properties of odd functions. How about EX-¹? Is that also zero? Why or why not? (b) (c) Find E[Z], E[X], E[|Z|³] and E[X³]. (d) Explain why E[Ze2²/2] is not zero even though h(z) = ze²²/2 is an odd function.
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Financial Accounting The Impact on Decision Makers
ISBN: 978-1305793194
10th edition
Authors: Gary A. Porter, Curtis L. Norton
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