(5 points) Consider two variables X and Y, show that E[X]=EY[EX[XY]] (5 points) Consider a random variable X, prove that E(X2)E(X)2 (10 points) Consider a nonnegative random variable X and a>0 show that P[Xa]aE[X]. Remark. This property implies an important theorem: Markov's Inequality. It gives an upper bound for the probability that a non-negative function of a random variable is greater than or equal to some positive constant, e.g. Markov's inequality shows that no more than 1/5 of the population can have more than 5 times the average income