We say that a random variable X is stochastically less than a random variable Y if P(X > x) x) for every r ER. 1. Show that if X is stochastically less than Y, Fx(x) 2 Fy(x) for every x E R, where Fx(x) and Fy(x) are the CDFs of the X and Y random variables, respectively. 2. Show that X is stochastically less than a + X for every a > 0. 3. Show that X is not stochastically less than aX for every a > 0. 4. Show that if X > 0 is a positive random variable, aX is stochastically less than X for every a