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.y1p(x, y)01 0.030 0.02050X3 0.090 0.0604 0.060 0.04020 0.015 0.010 0.0250.0502 0.075 0.050 0.1250.1500.1005 0.030 0.020 0.050(a) What is the probability that there is exactly one car and exactly one bus during a cycle?0.020(b) What is the probability that there is at most one car and at most one bus during a cycle?0.075(c) What is the probability that there is exactly one car during a cycle? Exactly one bus?P(exactly one car) = 0.220xP(exactly one bus) = 0.200(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?0.985X(e) Are X and Y independent rv's? Explain.O Yes, because p(x, y) = P(x) Py(Y).O Yes, because p(x, y) = Px(x) • P₂(Y).#● No, because p(x, y) = Px(x) • Py(y).O No, because p(x, y) = px(x) • P₂(y).X

Given the joint PMF of X and Y, and we have to find the probabilities of given events:

Answered: The joint probability distribution of…

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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