# Documentation

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# poisspdf

Poisson probability density function

## Syntax

`Y = poisspdf(X,lambda)`

## Description

`Y = poisspdf(X,lambda)` computes the Poisson pdf at each of the values in `X` using mean parameters in `lambda`. `X` and `lambda` can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions as the other input. The parameters in `lambda` must all be positive.

The Poisson pdf is

`$f\left(x|\lambda \right)=\frac{{\lambda }^{x}}{x!}{e}^{-\lambda }\text{\hspace{0.17em}};\text{\hspace{0.17em}}x=0,1,2,\dots ,\infty \text{\hspace{0.17em}}.$`

The density function is zero unless x is an integer.

## Examples

A computer hard disk manufacturer has observed that flaws occur randomly in the manufacturing process at the average rate of two flaws in a 4 GB hard disk and has found this rate to be acceptable. What is the probability that a disk will be manufactured with no defects?

In this problem, λ = 2 and x = 0.

```p = poisspdf(0,2) p = 0.1353```