MGF transform

Nov 2009
517
130
Big Red, NY
Just got out of my stats final. Question.

Suppose \(\displaystyle Z\sim -\frac{1}{h}e^{-\frac{z}{h}}.\)

How do I find the MGF, \(\displaystyle M_{\frac{1}{Z}}?\)

Do I have to transform \(\displaystyle Z,\) then use the definition of MGF? Or, is there some slick trick I'm missing here?
 

Moo

MHF Hall of Honor
Mar 2008
5,618
2,802
P(I'm here)=1/3, P(I'm there)=t+1/3
Hello,

What is -1/h e(-z/h) ? Is it supposed to be a pdf ? Because it's negative ! (Surprised)
And what is h ? And where is this - supposed to be - pdf defined ?
 
Nov 2009
517
130
Big Red, NY
Hello,

What is -1/h e(-z/h) ? Is it supposed to be a pdf ? Because it's negative ! (Surprised)
And what is h ? And where is this - supposed to be - pdf defined ?
Hi! (Happy)

The pdf was some funky exponential looking thing. I may not be remembering it correctly.

For definiteness lets just consider it to be:

\(\displaystyle Z\sim exp{(\frac{1}{h})}.\)

Now how to find \(\displaystyle M_{\frac{1}{Z}}?\)

Thanks.