Introduction to Probability · Problem 10.3.3

Markov Chains — Grinstead & Snell

Mathematics — Probability · moment-generating-functions-continuous

Problem

Let

X

be a continuous random variable with values in

[0, \infty)

and density

f_X

. Find the moment generating functions for

X

if (a)

f_X(x) = 2e^{-2x}

. (b)

f_X(x) = e^{-2x} + (1/2)e^{-x}

. (c)

f_X(x) = 4xe^{-2x}

. (d)

f_X(x) = \lambda(\lambda x)^{n-1} e^{-\lambda x}/(n-1)!