binopdf (Statistics Toolbox)

Binomial probability density function (pdf)

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 parameters in N and P. Vector or matrix inputs for X, N, and P must all have the same size. A scalar input is expanded to a constant matrix 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

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?

y = binopdf([0:200],200,0.02);
[x,i] = max(y);
i
i =
     5

binoinv binornd