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# binopdf

Binomial probability density function

## Syntax

Y = binopdf(X,N,P)

## Description

Y = binopdf(X,N,P) computes the binomial pdf at each of the values in X using the corresponding number of trials in N and probability of success for each trial in P. Y, N, and P 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 of the other inputs.

The parameters in N must be positive integers, and the values in P must lie on the interval [0, 1].

The binomial probability density function for a given value x and given pair of parameters n and p is

$y=f\left(x|n,p\right)=\left(\begin{array}{c}n\\ x\end{array}\right){p}^{x}{q}^{\left(n-x\right)}{I}_{\left(0,1,...,n\right)}\left(x\right)$

where q = 1 – p. The result, y, is the probability of observing x successes in n independent trials, where the probability of success in any given trial is p. The indicator function I(0,1,...,n)(x) ensures that x only adopts values of 0, 1, ..., n.

## Examples

A Quality Assurance inspector tests 200 circuit boards a day. If 2% of the boards have defects, what is the probability that the inspector will find no defective boards on any given day?

```binopdf(0,200,0.02)
ans =
0.0176```

What is the most likely number of defective boards the inspector will find?

```defects=0:200;
y = binopdf(defects,200,.02);
[x,i]=max(y);
defects(i)
ans =
4```