Problem 2. Let p > 0 be a real number. Consider function f which has values f(t) = Ct-P for t 1, and f(t) = 0 for t < 1. For which values of p we can select constant C so that this function f is a probability density function for some continuous random variable? For which values of p will this random variable have finite expectation? For which values of p will this random variable have finite variance?