Answer Happy

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 Z 1 0.025 0 0.010 0.015 1 0.030 0.020 0.050 0.050 0.125 2 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 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) = Plexactly 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) = x(x) Pylv). O Yes, because p(x, y) + x(x) - Py(y). O No, because p(x, y) = y(x). Pyly). O No, because p(x, y) + Py(x). Pyl).