# MGF transform

#### Anonymous1

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
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 ?

#### Anonymous1

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.