I'm wondering about the following problem: Let $\displaystyle $f_{X,Y,Z}(x,y,z)=e^{-(x+y+z)}$$ for x,y,z>0. Find $\displaystyle $P(X<Y<Z)$$. I've seen the solution to this at http://www-rohan.sdsu.edu/~babailey/.../lecture10.pdf, but I don't understand how they went from P(X<Y<Z) to the triple integral. How does one work with an expression as P(X<Y<Z)? Thanks.