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In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 25% osy<5 f(y) = 5 sys 10 0 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20k 0.20 0.20 0.20k 0.15 0.15 0.15 0.15 ÍZKEZA. 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 y 2 4 6 O 8 10 2 4 8 O 6 10 8 O 2 4 6 10 2 4 6 8 10 (b) Verify that t [*^ Ry) dy = 1. 10 f(y) dy= 5 525 (c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 9 min? 25

In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 25% osy<5 f(y) = 5 sys 10 0 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20k 0.20 0.20 0.20k 0.15 0.15 0.15 0.15 ÍZKEZA. 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 y 2 4 6 O 8 10 2 4 8 O 6 10 8 O 2 4 6 10 2 4 6 8 10 (b) Verify that t [*^ Ry) dy = 1. 10 f(y) dy= 5 525 (c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 9 min? 25

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Solve part B through F

In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 0 ≤ y < 5 f(y) = # 5 ≤ y ≤ 10 25 0 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20 0.20 0.20 0.20k 0.15 0.15 0.15 0.15 IZUIZN 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 V y y 2 4 6 8 10 O 2 4 6 8 10 2 4 6 8 10 4 6 8 10 (b) Verify that f(y) dy = 1. + [° F(x) [Andy=[ 10 5 = 1/2+ (c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 9 min? (e) What is the probability that total waiting time is between 3 and 9 min? (f) What is the probability that total waiting time is either less than 4 min or more than 7 min?
Transcribed Image Text:In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5, then it can be shown that the total waiting time Y has the pdf below. 0 ≤ y < 5 f(y) = # 5 ≤ y ≤ 10 25 0 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) f(y) f(y) f(y) 0.20 0.20 0.20 0.20k 0.15 0.15 0.15 0.15 IZUIZN 0.10 0.10 0.10 0.10 0.05 0.05 0.05 0.05 V y y 2 4 6 8 10 O 2 4 6 8 10 2 4 6 8 10 4 6 8 10 (b) Verify that f(y) dy = 1. + [° F(x) [Andy=[ 10 5 = 1/2+ (c) What is the probability that total waiting time is at most 3 min? (d) What is the probability that total waiting time is at most 9 min? (e) What is the probability that total waiting time is between 3 and 9 min? (f) What is the probability that total waiting time is either less than 4 min or more than 7 min?
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