Let X be a random variable with expected value E[X] = X and variance V[X] = 2 X . (a) The variance of X is defined as 2 X = E[(X X )2]. Show that it can also be written as 2 X = E[X2] 2 X . (b) Show that if a is any number distinct from X , then E[(X X )2] < E[(X a)2]