How do you show that the exponential function is its own derivative by using the fact that E(x)E(y)=E(x+y). Don't assume the derivative exists either. You can use any other property of E(x) that you can think of, but you are supposed to use the fact above primarily. (that is, without using the obvious power series expansion argument) I think it must be something so obvious that I am missing it altogether! Thanks for the help. Oh, and while you're at it, how would I then show that E(x) is convex?