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Problem 4. Let X be a random variable with EIXI4 < oo. Define μ1 = EX and Alk-E(X-μ)k, k 2, 3, 4, and then 03 = 쓺 (skewness), a,--2 (kurtosis) 3/2 (1) Show that if P(X- > z) = P(X-円く-r) for every x > 0, then μ3-0, but not the other way around. (2) Compute as and a when X is Binomial with parameter p, exponential with mean1, uniform on [O, 1], standard normal, and double exponential (fx (x)-(1/2)e-M).

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Answer #1

0o Oo 7ぃーー

从-o ~乇 13 8. t 1 ジC2- 2. u,从) P2 (2-b) 2.

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