3.77 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 f(x, y) =

9 16

· 1 4(x+y ) , 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?