Question: If we let a = µ in the first part of Theorem 4.10 on page 128, where µ is the mean of X, we get

If we let a = €“ µ in the first part of Theorem 4.10 on page 128, where µ is the mean of X, we get

(a) Show that the rth derivative of MX €“ µ(t) with respect to t at t = 0 gives the rth moment about the mean of X.
(b) Find such a generating function for moments about the mean of the binomial distribution, and verify that the second derivative at t = 0 is nÎ¸(1 €“ Î¸).

-ut. Mx() - Mx-p(0 My()

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