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Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a a = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter µ = 8t. a) What is the probability that exactly 6 small aircraft arrive during a 1- hour period? At least 6? At least 10? b) What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period? c) What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? That at most 10 arrive during this period?

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a a = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter µ = 8t. a) What is the probability that exactly 6 small aircraft arrive during a 1- hour period? At least 6? At least 10? b) What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period? c) What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? That at most 10 arrive during this period?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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( Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a a = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter µ = 8t. a) What is the probability that exactly 6 small aircraft arrive during a 1- hour period? At least 6? At least 10? b) What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period? c) What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? That at most 10 arrive during this period? 37
Transcribed Image Text:( Suppose small aircraft arrive at a certain airport according to a Poisson process with rate a a = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter µ = 8t. a) What is the probability that exactly 6 small aircraft arrive during a 1- hour period? At least 6? At least 10? b) What are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period? c) What is the probability that at least 20 small aircraft arrive during a 2.5-hour period? That at most 10 arrive during this period? 37
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