Moment Generating Function:
The moment generation function is associated with a probability distribution. The moment generating function can be used to generate moments. However, the main use of the moment generating function is not in generating moments but to help in characterizing a distribution.
The moment generating function of a random variable X , denoted by MX(t), is defined as:
Mx(t) = E(etx),
provided the expectation exists for t in some neighborhood of 0.