Theorem: Let F(x) be the distribution function of X. If X is any r.v. (discrete, continuous, or mixed) defined on the interval [a,∞) (or some subset of it), then E(X)= ∞ ∫ [1 - F(x)]dx + a a 1) Is this formula true for any real number a? In particular, is it true for a<0? 2) When is this formula ever useful (computationally)? Why don't just get the density function then integrate to find E(X)? Thanks for clarifying!