equals the probability of at most hits during an interval for which A is the expected value of the number of hits.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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In a Poisson process with rate parameter \(\lambda\), the expression

\[
e^{-\lambda} \left( 1 + \lambda + \frac{\lambda^2}{2!} + \cdots + \frac{\lambda^8}{8!} \right)
\]

equals the probability of at most \([ \text{Blank} ]\) hits during an interval for which \(\lambda\) is the expected value of the number of hits.
Transcribed Image Text:In a Poisson process with rate parameter \(\lambda\), the expression \[ e^{-\lambda} \left( 1 + \lambda + \frac{\lambda^2}{2!} + \cdots + \frac{\lambda^8}{8!} \right) \] equals the probability of at most \([ \text{Blank} ]\) hits during an interval for which \(\lambda\) is the expected value of the number of hits.
Expert Solution
Step 1

Let , X\to Poisson(\lambda)

The probability mass function of X is  

P(X=x)=\frac{e^{-\lambda}\lambda^x}{x!};x\geq 0 , \lambda>0

Our aim is to fill the blank.

 

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