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 2 C 0.010 0.025 0.015 0.020 0.050 0.030 2 0.050 0.125 0.075 X 3 0.060 0.150 0.090 4 0.040 0. 100 0.060 5 0.020 0.050 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. O Yes, because p(x, y) = Px(x) . Py(y). O Yes, because p(x, y) # Px(x) . Py(y). O No, because p(x, y) = Px(x) . Py(y). O No, because p(x, y) = Px(x) . Py(y)