Introduction to Probability · Problem 10.3.4

Markov Chains — Grinstead & Snell

Mathematics — Probability · moment-generating-functions-continuous

Problem

For each of the densities in Exercise 3, calculate the first and second moments,

\mu_1

and

\mu_2

, directly from their definition and verify that

g(0) = 1

g'(0) = \mu_1

, and

g''(0) = \mu_2