6.5 Method of Moment Generating Function PDF

Preview

Summary

Lucas Godoy...

Description

The moment generating function method for finding the probability distribution of a function of random variables is based on uniqueness theorem: Theorem 6.1 (Uniqueness theorem): Let m (t) and m (t) denote the moment generating functions of random variables X and Y. If both moment generating functions exist and m (t) = m (t) for all values t, then X and Y have the same probability distribution • If U is a function of n random variables, Y , Y , ..., Y generating function

the first step in using the theorem is to find the moment

• Once the moment generating function for U has been found it’s compared with the moment generating functions for random variables Example 6.10 Suppose Y ~ N(

More notes online

,

) show that

has normal distribution with mean 0 and variance 1...