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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) a 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. f(y) = 2 5 0.15 1 25 0 1 25 0 ≤y<5 5 ≤ y ≤ 10 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) 0.20k f(y) 0.20 0.15

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) a 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. f(y) = 2 5 0.15 1 25 0 1 25 0 ≤y<5 5 ≤ y ≤ 10 y <0 or y> 10 (a) Sketch a graph of the pdf of Y. f(y) 0.20k f(y) 0.20 0.15

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please solve a, b, c, d, e, and 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 5, then it can be shown that the total waiting time Y has the pdf below. has a uniform distribution with A = 0 and B = f(y) f(y) 0.20 0.15 0.10 (a) Sketch a graph of the pdf of Y. 0.05 f(y) f(y) 0.20 0.15 VV 0.10 0.05 y 10 0.20 0.15 0.10 0.05 2 (b) Verify that ["anor=[ f(y) dy = 1 25 2 - 2 0 + [ f(y) 1 25 4 4 0 ≤ y ≤ 5 5 ≤ y ≤ 10 y <0 or y> 10 f(y) dy = 1. 5 0 6 6 + 8 co 8 10 10 5 f(y) 0.20 0.15 0.10 0.05 2 2 4 4 6 8 6 8 y 10 10 y
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 5, then it can be shown that the total waiting time Y has the pdf below. has a uniform distribution with A = 0 and B = f(y) f(y) 0.20 0.15 0.10 (a) Sketch a graph of the pdf of Y. 0.05 f(y) f(y) 0.20 0.15 VV 0.10 0.05 y 10 0.20 0.15 0.10 0.05 2 (b) Verify that ["anor=[ f(y) dy = 1 25 2 - 2 0 + [ f(y) 1 25 4 4 0 ≤ y ≤ 5 5 ≤ y ≤ 10 y <0 or y> 10 f(y) dy = 1. 5 0 6 6 + 8 co 8 10 10 5 f(y) 0.20 0.15 0.10 0.05 2 2 4 4 6 8 6 8 y 10 10 y
(b) Verify that [ FLY -∞ 2 [ F(X) f(y) dy = f(y) dy = 1. = = 1/2 + ( 0 6 8 + 10 y.. 105 (c) What is the probability that total waiting time is at most 3 min? 2.0 (d) What is the probability that total waiting time is at most 7 min? (e) What is the probability that total waiting time is between 3 and 7 min? 2 4 (f) What is the probability that total waiting time is either less than 2 min or more than 8 min? 6 8 10 y
Transcribed Image Text:(b) Verify that [ FLY -∞ 2 [ F(X) f(y) dy = f(y) dy = 1. = = 1/2 + ( 0 6 8 + 10 y.. 105 (c) What is the probability that total waiting time is at most 3 min? 2.0 (d) What is the probability that total waiting time is at most 7 min? (e) What is the probability that total waiting time is between 3 and 7 min? 2 4 (f) What is the probability that total waiting time is either less than 2 min or more than 8 min? 6 8 10 y
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