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Suppose the you have to take a bus to work. The amount of time until the next bus arrives follows an Exponential distribution with mean 7 minutes. (a) What is the probability that the next bus will arrive within 5 minutes? (b) 90% of all buses arrive within how many minutes of the previous bus? (c) Suppose the bus still has not arrived within 9 minutes of the last bus. Knowing that, what is the probability that the next bus will take at least 15 minutes to arrive? (d) Suppose that the amount of time the next bus arrives is independent of each next bus with the same distribution (Exponential with mean 7). What is the probability that the next bus arrives in less time than the next next bus (i.e. a second bus)?

Suppose the you have to take a bus to work. The amount of time until the next bus arrives follows an Exponential distribution with mean 7 minutes. (a) What is the probability that the next bus will arrive within 5 minutes? (b) 90% of all buses arrive within how many minutes of the previous bus? (c) Suppose the bus still has not arrived within 9 minutes of the last bus. Knowing that, what is the probability that the next bus will take at least 15 minutes to arrive? (d) Suppose that the amount of time the next bus arrives is independent of each next bus with the same distribution (Exponential with mean 7). What is the probability that the next bus arrives in less time than the next next bus (i.e. a second bus)?

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 (d) part
Suppose the you have to take a bus to work. The amount of time until the next bus arrives follows an Exponential distribution with mean 7 minutes. (a) What is the probability that the next bus will arrive within 5 minutes? (b) 90% of all buses arrive within how many minutes of the previous bus? (c) Suppose the bus still has not arrived within 9 minutes of the last bus. Knowing that, what is the probability that the next bus will take at least 15 minutes to arrive? (d) Suppose that the amount of time the next bus arrives is independent of each next bus with the same distribution (Exponential with mean 7). What is the probability that the next bus arrives in less time than the next next bus (i.e. a second bus)?
Transcribed Image Text:Suppose the you have to take a bus to work. The amount of time until the next bus arrives follows an Exponential distribution with mean 7 minutes. (a) What is the probability that the next bus will arrive within 5 minutes? (b) 90% of all buses arrive within how many minutes of the previous bus? (c) Suppose the bus still has not arrived within 9 minutes of the last bus. Knowing that, what is the probability that the next bus will take at least 15 minutes to arrive? (d) Suppose that the amount of time the next bus arrives is independent of each next bus with the same distribution (Exponential with mean 7). What is the probability that the next bus arrives in less time than the next next bus (i.e. a second bus)?
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