A random variable is said to follow a Uniform (a, b) distribution if it is equally likely to take on any value in the range [a, b] and never takes a value outside this range. Suppose that X is such a random variable, i.e., X Uniform (a, b). The pdf of X is f (x) = 1/(ba) for a x b, and zero elsewhere. (a) Calculate E [X ]. (b) Using the shortcut formula, show that Var (X ) = (b a)2/12. [Hint: In caculating E X 2, recall that b3 a3 can be factorized as (b a)(b2 + a2 + ab)