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.
p(x, y) 0 1 2
x 0 0.025 0.010 0.015
1 0.050 0.020 0.030
2 0.125 0.050 0.075
3 0.150 0.060 0.090
4 0.100 0.040 0.060
5 0.050 0.020 0.030
(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?
P(exactly one car) =
P(exactly one bus) =
(d) Suppose the left-turn lane is to have a capacity of five cars and 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.
Yes, because p(x, y) = pX(x) � pY(y).
Yes, because p(x, y) ? pX(x) � pY(y).
No, because p(x, y) = pX(x) � pY(y).
No, because p(x, y) ? pX(x) � pY(y).