Hello everyone!

I've got this problem on multivariable distributions I'm stuck on...

Let

denote a random sample of size n = 3 from a distribution with the geometric pdf

and given the distribution

Question find the pdf of

then find

.

Now I considered using the moment generating function for 3 reasons: (a)

are a random sample size

are independent (b) they have the same pdf thus mgf, and (c) well, mgf can be used for this.

So i started out like this:

Then I got stuck there... I presume I don't know how to "transform" variables in descrete distributions unlike continuous ones.

So any help is much appreciated!