Introduction to Probability · Problem 10.3.7

Markov Chains — Grinstead & Snell

Mathematics — Probability · moment-generating-functions-continuous

Problem

Let

X

be a continuous random variable with values in

[0, 1]

, uniform density function

f_X(x) \equiv 1

and moment generating function

g(t) = (e^t - 1)/t

. Find in terms of

g(t)

the moment generating function for (a)

-X

. (b)

1 + X

. (c)

3X

. (d)

aX + b