Question: X is a random variable with moments E(X), E(X2), E(X3), and so forth. (a) Show E(X - )3 = E(X3) - 3[E(X2)][E(X)] + 2[E(X)]3. (b)

X is a random variable with moments E(X), E(X2), E(X3), and so forth.
(a) Show E(X - µ)3 = E(X3) - 3[E(X2)][E(X)] + 2[E(X)]3.
(b) Show E(X - µ)4 = E(X4) - 4[E(X)][E(X3)] + 6] E(X)]2[E(X2)] - 3[E(X)]4.

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