# Math Help - Moment Generating function of a normal variable

1. ## Moment Generating function of a normal variable

Hi everybody,

Again a problem with deriving an MGF.

I don't understand the manipulation in the first row. Why is e^xt disappearing? Why do we choose to make this (yellow marked) specific substitution....µ = µ + σ^2*t.

[IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
[IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]
[IMG]file:///C:/Users/Marmy/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif[/IMG]

2. ## Re: Moment Generating function of a normal variable

Originally Posted by Marmy
Hi everybody,

Again a problem with deriving an MGF.

I don't understand the manipulation in the first row. Why is e^xt disappearing? Why do we choose to make this (yellow marked) specific substitution....µ = µ + σ^2*t.