Thread: 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.


Thanks for your help! [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]

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.


Thanks for your help! [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]

The e^(xt) has not disappeared. Expand the exponent in the second integral and it clearly appears.

The reason for the substitution is clear from the entire solution ....

Thanks,

I managed to understand this problem now!