Grinstead-Snell-Probability · Problem 10.3.9

Markov Chains

Mathematics · moment-generating-functions-continuous

Problem

Let

X_1, X_2, \ldots, X_n

be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a)

X_1

. (b)

S_2 = X_1 + X_2

. (c)

S_n = X_1 + X_2 + \cdots + X_n

. (d)

A_n = S_n/n

. (e)

S_n^* = (S_n - n\mu)/\sqrt{n\sigma^2}