Introduction to Probability · Problem 10.3.1

Markov Chains — Grinstead & Snell

Mathematics — Probability · moment-generating-functions-continuous

Problem

Let

X

be a continuous random variable with values in

[0, 2]

and density

f_X

. Find the moment generating function

g(t)

for

X

if (a)

f_X(x) = 1/2

. (b)

f_X(x) = (1/2)x

. (c)

f_X(x) = 1 - (1/2)x

. (d)

f_X(x) = |1 - x|

. (e)

f_X(x) = (3/8)x^2

. Hint: Use the integral definition, as in Examples 10.15 and 10.16.