a problem regarding maximum and minimum of two positive random variables
Suppose X and Y are two positive random numbers.
Define U = max(X, Y ) and V = min(X, Y )
Show that:
(a) E(X)E(Y ) >= E(U)E(V ):
(b) Var(X) + Var(Y )>= Var(U) + Var(V )
I am not able to solve this problem...can you help me?? thanks...