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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
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Assume that Y denotes the number of bacteria per cubic

Chapter 5, Problem 138E

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QUESTION:

Problem 138E

Assume that Y denotes the number of bacteria per cubic centimeter in a particular liquid and that Y has a Poisson distribution with parameter λ. Further assume that λ varies from location to location and has a gamma distribution with parameters α and β, where α is a positive integer. If we randomly select a location, what is the

a expected number of bacteria per cubic centimeter?

b standard deviation of the number of bacteria per cubic centimeter?

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QUESTION:

Problem 138E

Assume that Y denotes the number of bacteria per cubic centimeter in a particular liquid and that Y has a Poisson distribution with parameter λ. Further assume that λ varies from location to location and has a gamma distribution with parameters α and β, where α is a positive integer. If we randomly select a location, what is the

a expected number of bacteria per cubic centimeter?

b standard deviation of the number of bacteria per cubic centimeter?

ANSWER:

Step 1 of 3

Given:

The variable Y represents the number of bacteria per cubic centimeter in a particular liquid.

The variable Y follows the Poisson distribution with parameter .

Assume that  varies from location to location and has a gamma distribution with parameters   and .

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