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 :)