The joint probability distribution of the number of cars X and the number of buses Y per signal cycle at aproposed left-turn lane is displayed in the accompanying joint probability table.y120.0250.0150.0100.0500.0300.0200.1250.0750.05030.1500.0900.06040.1000.0600.04050.0500.0300.020What is the probability that there are exactly two cars during a cycle?10%25%5%O 30%1,2.

It is given that the variable x denotes the number of cars and the y denotes number of buses.

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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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, у) 1 2 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 0.030 0.020 0.050 (a) What is the probability that there 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. Yes, because p(x, y) = Px(x) · Py(y). Yes, because p(x, y) ± Px(x) · py(y). No, because p(x, y) = Px(x) · Py(Y). No, because p(x, y) # Px(x) · Py(y).
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The joint probability distribution of two random variables X, Y is given in the table below. Y=-3 Y=2 Y=4 X=-4 0.02 0.14 0.13 X=-2 0.05 0.01 0.05 X=-1 0.09 0.00 0.11 X=1 0.12 0.15 0.07 X= 3 0.06 0.00 0.00 From the information in the table, calculate each of the following three probabilities. (a) P(Y> 2) = [ (b) P(X < 1,Y = 2) = | (c) P(Y< -3) = [] I Don't Know Submit O 2022 to search ALEKS - Britney Fri.
Construct the marginal probability distribution of Y. What is the mean of X and Y .

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