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Statistics / Mathematical Statistics with Applications 7 / Chapter 3 / Problem 210SE

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

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Chapter 3, Problem 210SE

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QUESTION:

Calculate \(P(|Y-\lambda| \leq 2 \sigma\) for the Poisson probability distribution of Example 3.22. Does this agree with the empirical rule?

Equation transcription:

$P(|Y-\lambda{}|\leq{}2\sigma{}$

Text transcription:

P(|Y-\lambda| \leq 2 \sigma

Questions & Answers

QUESTION:

Calculate \(P(|Y-\lambda| \leq 2 \sigma\) for the Poisson probability distribution of Example 3.22. Does this agree with the empirical rule?

Equation transcription:

$P(|Y-\lambda{}|\leq{}2\sigma{}$

Text transcription:

P(|Y-\lambda| \leq 2 \sigma

ANSWER:

Solution:

Step 1 of 3:

It is given that the number of accidents per month Y is a Poisson random variable with mean 6.

Then the probability mass function of Y is

P(Y)= $\frac{{e}^{-\lambda{}}{\lambda{}}^{y}}{y!}$

Using this we need to calculate P(|Y- $\lambda{}$ | $\leq{}2\sigma{}$ ) and then we have to compare it with the empirical rule.

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