 
Summary: Moment Generating Functions: a first look
Math431, Spring 2011
Instructor: David F. Anderson
Section 7.7: Moment generating functions a first look
Moment generating functions have two major properties:
1. They allow us to calculate the moments of random variable.
2. No two different RVs have same moment generating function. Thus, to prove a RV
has a certain distribution, you really only need moment generating function.
Definition: For a random variable X, the moment generating function of X is
MX(t) = E etX
.
Therefore, for discrete, continuous RV we have
MX(t) =
xR(X)
etx
pX(x) discrete case
MX(t) =

etx
