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

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Statistics

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

y

p(x,y)

    		012
x0    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 andexactly one bus during a cycle?


(b) What is the probability that there is at most one car and atmost one bus during a cycle?


(c) What is the probability that there is exactly one car during acycle? Exactly one bus?

P(exactly one car)=
P(exactly one bus)=


(d) Suppose the left-turn lane is to have a capacity of five carsand one bus is equivalent to three cars. What is the probability ofan overflow during a cycle?


(e) Are X and Y independent rv's? Explain.

Yes, because p(x, y) =pX(x) ·pY(y).Yes, becausep(x, y) ≠pX(x) ·pY(y).    No,because p(x, y) =pX(x) ·pY(y).No, becausep(x, y) ≠pX(x) ·pY(y).

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