You need to make a 2-2 transformation.
you let Y=B-A and it didn't work with X=B+A?
Then maybe letting X=B might be better.
After that you need to integrate out the X rv.
Why don't you post what you've done and I'll look at it.
Hi
I need to work out the pdf of B-A, where A~exp(alpha) and B~exp(beta). I've tried making a substitution into their joint density of X=A+B, Y=B-A but... It doesn't seem to be working. I get dependencies on whether alpha is greater than beta (which I have no information about) and everything breaks down if alpha=beta.
Can you talk me through/show me how to get the pdf? Thanks
Ok, trying it with Y=B-A and X=B I get:
Pdf of y to be [(alpha*beta)/(alpha+beta)] *exp(alpha*y)
To get this, I integrated the joint pdf of a,b, which I assume is (alpha*beta)*exp(-alpha*a -beta*b) wrt x after making the substitution. (Jacobian=1). I integrated it between infinite and zero.
Again, I don't think this answer is correct. It doesn't depend on which is bigger, alpha or beta, but... Y should be on the range infinite to minus infinite, and integrating my above pdf on that range doesn't give 1.
Thanks for any help.