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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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Astronomers treat the number of stars in a given volume of

Chapter 3, Problem 161E

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QUESTION:

Problem 161E

Astronomers treat the number of stars in a given volume of space as a Poisson random variable. The density in the Milky Way Galaxy in the vicinity of our solar system is one star per 16 cubic light-years.

(a) What is the probability of two or more stars in 16 cubic light-years?

(b) How many cubic light-years of space must be studied so that the probability of one or more stars exceeds 0.95?

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QUESTION:

Problem 161E

Astronomers treat the number of stars in a given volume of space as a Poisson random variable. The density in the Milky Way Galaxy in the vicinity of our solar system is one star per 16 cubic light-years.

(a) What is the probability of two or more stars in 16 cubic light-years?

(b) How many cubic light-years of space must be studied so that the probability of one or more stars exceeds 0.95?

ANSWER:

Solution:

Step 1 of 3:

Let X follows the Poisson distribution with the density

P(X = x) =

Let X = number of stars per 16 cubic light years

= 1.

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