1. The problem statement, all variables and given/known data Let f(x1, x2, x3) = e-(x1+x2+x3), 0<x1,2,3<infinity, zero elsewhere be a joint pdf of X1, X2, X3. Compute P(X1< X2< X3) and P(X1= X2< X3) Determine the joint mgf. 3. The attempt at a solution P(X1< X2< X3) = triple integral of e-(x1+x2+x3) dx2dx1dx3 as x2 goes from x1 to x3, x1 goes from 0 to x2 and x3 goes from x2 to infinity. When I solve this integral I get 0 for an answer. The back of the book suggests the answer is 1/6. Clearly, I am setting up the problem wrong, but I don't know where my mistake is. Similarly, I'm having trouble setting up the second part of the question as well. Joint mgf = E(et1x1+t2x2+t3x3) but this integral is not easy by hand. Is there another way to do it?