Grinstead-Snell-Probability · Problem 10.3.10

Markov Chains

Mathematics · moment-generating-functions-continuous

Problem

Let

X_1, X_2, \ldots, X_n

be an independent trials process with density

f(x) = \frac{1}{2}e^{-|x|}, \quad -\infty < x < +\infty.

(a) Find the mean and variance of

f(x)

. (b) Find the moment generating function for

X_1

S_n

A_n

, and

S_n^*

. (c) What can you say about the moment generating function of

S_n^*

n \to \infty

? (d) What can you say about the moment generating function of

A_n

n \to \infty