Introduction to Probability · Problem 10.1.2

Generating Functions — Grinstead & Snell

Mathematics — Probability · generating-functions-discrete

Problem

For each of the distributions (a) through (d) of Exercise 1 calculate the first and second moments,

\mu_1

and

\mu_2

, directly from their definition, and verify that

h(1) = 1

h'(1) = \mu_1

, and

h''(1) = \mu_2 - \mu_1