Question

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	1	2
x	0	0.010	0.015	0.025
	1	0.020	0.030	0.050
	2	0.050	0.075	0.125
	3	0.060	0.090	0.150
	4	0.040	0.060	0.100
	5	0.020	0.030	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) = p_X(x) · p_Y(y).Yes, because p(x, y) ≠ p_X(x) · p_Y(y).    No, because p(x, y) = p_X(x) · p_Y(y).No, because p(x, y) ≠ p_X(x) · p_Y(y).

Answer 1