Question

The joint probability distribution of the number X of cars and the number Y of buses...

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) = 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).

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