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.
y p(x, y)
0 0.015 0.010 0.025
1 0.030 0.020 0.050
2 0.075 0.050 0.125
3 0.090 0.060 0.150
4 0.060 0.040 0.100
5 0.030 0.020 0.050
(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).