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Let X₁ and X₂ be independent Poisson random variables with parameters A₁ and A₂. a) Show that for every n ≥ 1, the conditional distribution of X₁, given X₁ + X₂ = n, is binomial, and find the parameters of this binomial distribution. b) The number of eggs laid by a certain kind of insect follows a Poisson distribution quite closely. It is known that two such insects have laid their eggs in a particular area. If the total number of eggs in the area is 150, what is the chance that the first insect laid at least 90 eggs? (State your assumptions, and give an approximate decimal answer.)

Let X₁ and X₂ be independent Poisson random variables with parameters A₁ and A₂. a) Show that for every n ≥ 1, the conditional distribution of X₁, given X₁ + X₂ = n, is binomial, and find the parameters of this binomial distribution. b) The number of eggs laid by a certain kind of insect follows a Poisson distribution quite closely. It is known that two such insects have laid their eggs in a particular area. If the total number of eggs in the area is 150, what is the chance that the first insect laid at least 90 eggs? (State your assumptions, and give an approximate decimal answer.)

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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Let X₁ and X₂ be independent Poisson random variables with parameters A₁ and A₂. a) Show that for every n ≥ 1, the conditional distribution of X₁, given X₁ + X₂ = n, is binomial, and find the parameters of this binomial distribution. b) The number of eggs laid by a certain kind of insect follows a Poisson distribution quite closely. It is known that two such insects have laid their eggs in a particular area. If the total number of eggs in the area is 150, what is the chance that the first insect laid at least 90 eggs? (State your assumptions, and give an approximate decimal answer.)
Transcribed Image Text:Let X₁ and X₂ be independent Poisson random variables with parameters A₁ and A₂. a) Show that for every n ≥ 1, the conditional distribution of X₁, given X₁ + X₂ = n, is binomial, and find the parameters of this binomial distribution. b) The number of eggs laid by a certain kind of insect follows a Poisson distribution quite closely. It is known that two such insects have laid their eggs in a particular area. If the total number of eggs in the area is 150, what is the chance that the first insect laid at least 90 eggs? (State your assumptions, and give an approximate decimal answer.)
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