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If we let a in the first

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 nθ(1 – θ).

(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 nθ(1 – θ).

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