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 for x = 0, 1, 2, … and y = 0, 1, 2, ….

1. Are the two random variables X and Y independent? Explain why or why not.

2. What is the probability that during the time period in question less than 4 vehicles arrive at the two street corners?

X1 1 1 2

1