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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 0 0.010 0.025 0.015 1 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) =

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 0 0.010 0.025 0.015 1 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) =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 0.010 0.025 0.015 1 0.020 0.050 0.030 2 0.050 0.125 0.075 3 0.060 4 0.150 0.090 0.100 0.020 0.050 0.040 0.060 5 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). Py(y). O No, because p(x, y) ‡ Px(x) • 0
Transcribed Image Text: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 0.010 0.025 0.015 1 0.020 0.050 0.030 2 0.050 0.125 0.075 3 0.060 4 0.150 0.090 0.100 0.020 0.050 0.040 0.060 5 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). Py(y). O No, because p(x, y) ‡ Px(x) • 0
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