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Let X and Y be random variables. The covariance of X and Y is defined by cov (X, Y) = E[(X - E(X)) (Y - E(Y))]. (a) Show that cov(X, Y) = E(XY) - E(X)E(Y). (b) Show that cov(X, Y) = 0 if X and Y are independent. (Note: the converse is not always true.) (c) Suppose you roll two four-sided dice. Let X be the outcome on the first die, and let Y be the sum of the outcomes of the two dice. Calculate cov(X, Y). (d) Is it possible to calculate the covariance between a discrete random variable and a con- tinuous random variable? For example, can you calculate the covariance between the number of customers arriving in a shop in a given time interval, and their interarrival times? Why or why not