P(x, y) 1 0.010 0.015 0.025 1. 0.020 0.030 0.050 0.050 0.075 0.125 3 0.060 0.090 0.150 4 0.040 0.060 0.100 0.020 0.030 0.050 (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) =
P(x, y) 1 0.010 0.015 0.025 1. 0.020 0.030 0.050 0.050 0.075 0.125 3 0.060 0.090 0.150 4 0.040 0.060 0.100 0.020 0.030 0.050 (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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
p(x, y)
1
2
0.010
0.015
0.025
1
0.020
0.030
0.050
2
0.050
0.075
0.125
0.060
0.090
0.150
4
0.040
0.060
0.100
0.020
0.030
0.050
(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.
Yes, because p(x, y) = Px(x) · Py(y).
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).
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