If we let a micro in the first part of Theorem 4 10 on page 128, where micro is the mean of X, we get (a) Show that the rth derivative of MX micro (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 dis...

If we let a = µ in the first part of Theorem 4.10 on page 128, where

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

(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¸).