The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table.

a. What is the probability that there is exactly one car and exactly one bus during a cycle?
b. What is the probability that there is at most one car and at most one bus during a cycle?
c. What is the probability that there is exactly one car during a cycle? Exactly one bus?
d. Suppose the left-turn lane is to have a capacity of five cars, and that one bus is equivalent to three cars. What is the probability of an overflow during a cycle?
e. Are X and Y independent rv's? Explain.

Transcribed Image Text:

px, y) 0025 2125 100 .015 .010 1050 .030 .020 050 060 040 030.020 075 090