Poisson Distribution

A Poisson Distribution gives the probability of an event happening based on an average occurrence of that event over a period of time or a large volume.

The formula for a poisson distribution is \[ P(X;\lambda) = \frac { e^{-\lambda} \lambda^{X}}{X!} \]

• lambda is the mean occurrence of that event.
• e is a constant = 2.7183.

Example:

There are 200 typos in a book that’s 500 pages, what is the probability of finding 3 errors on 1 page?

\[ \lambda = 200/500 = 0.4\]

dpois(3, 0.4)

## [1] 0.00715008

Example:

Say there are 10 typos in a book that’s 200 pages, what is the probability of finding 2 errors on 1 page.

Lambda is the average or 10/200 = .05

dpois(2,.05)

## [1] 0.001189037