Important Identity for Expected Value: For a non-negative cont's random variable X with the PDF fX(x) show that E[X] = Z 0 F c X(x)dx, where F c X(x) := 1 FX(x). Remark (don't need to show this): you can show a similar identity for discrete R.V.s. I.e., E[X] = X xkS F c X(xk), where S = {x | pX(x) 6= 0} is the support of the random variable