8. (25 points) Consider the random variables X and Y that represent the number of vehicles that arrive at two separate street corners during a certain 2-minute period. These street corners are fairly close together so it is important that traffic engineers deal with them jointly if necessary. The joint distribution of X and Y is known to be fxy(x, y) = 4xty+2' for x = 0, 1, 2, . .., and y = 0, 1, 2, .. . (a) Are the two random variables X and Y independent? Explain why or why not. (b) What is the probability that during the time period in question less than 4 vehicles arrive at the two street corners? (Ans: 63/64)