Thread: Joint Moment Generating Function

Hello,
I have my final coming up and I am looking to review the joint moment generating function. I know the definition of the joint moment generating function namely E[exp(t1*x+t2*y)] but do not understand how to use this in problems that are complicated.

Can anyone explain to me how to find joint moment generating functions by solving this example or giving me a link to where examples of joint moment generating functions are found.

Here is one problem that I need to know for the final.

If f(x,y)= [y/sqrt(2*pi)]*exp(-y-(.5*(x-y)^2)) then what is the joint mgf of X and Y.

Thank You Very Much

First of all I need to know the support.
I'm guessing that y>0 and x is any real number.

Y>0, X any real number