# Statistics: Moment Generating Function

It is attached it is to show that if all Xi are normally distributed then

Y=a1X1+a2X2+...+anXn

Also is normally distributed

But please see the attachment as the question is a bit more specific than that as well. Thanks

File is uploaded in pdf and word

© BrainMass Inc. brainmass.com October 10, 2019, 7:27 am ad1c9bdddfhttps://brainmass.com/statistics/statistical-theory/statistics-moment-generating-function-581973

#### Solution Preview

We will use the following properties:

Lemma 1

If , then =

Lemma 2

If X and Y are independent, then

...

#### Solution Summary

Prove, using MGM, that a sum of independent normally distributed variables is also normal.

$2.19