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Chapter 5: Q5.4-4E (page 296)

Suppose that in a certain book there are, on average,位misprints per page and that misprints occurred according to a Poisson process. What is the probability that a particular page will contain no misprints?

Short Answer

Expert verified

The probability of containing no misprints on a particular page is \({e^{ - \lambda }}\).

Step by step solution

01

Given information

The number of misprints in a certain book follows a Poisson distribution with mean \(\lambda \).

02

Compute the probability

If \(f\left( {x|\lambda } \right)\) be the p.f of Poisson distribution with mean \(\lambda \), then the probability of containing no misprints on a particular page in a certain book is

\(\begin{array}{c}P\left( {X = 0} \right) = f\left( {0|\lambda } \right)\\ = \frac{{{e^{ - \lambda }}{\lambda ^0}}}{{0!}}\\ = {e^{ - \lambda }}\end{array}\)

Therefore, there is a probability of containing no misprints on a particular page in a certain book \({e^{ - \lambda }}\).

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