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Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of the

Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of the

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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Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of them were red?
Transcribed Image Text:Assume that the number of bikes arriving at the campus follows a Poisson process with a rate of 200 per hour. Out of those bikes, 5% are red and 95% have other colors. (i) What is the probability that 20 red bikes arrive within an hour? (ii) What is the probability that 20 red bikes arrive within the first hour and 500 bikes (of any color) arrive within the first three hours? (iii) Given that 20 red bikes arrived within an hour, what is the expected total number of bikes that arrived within this hour? (iv) Given that 150 bikes arrived within an hour, what is the probability that exactly 10 out of them were red?
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