# 3.5.3.2.2 Binopdf

## Definition:

bnp = binopdf(x, nt, p) returns the probability density function of the binomial distribution with parameters nt and p.

$f(x|nt, p) = \left( \begin{matrix} nt \\ x \end{matrix}\right) p^x (1-p)^{nt-x},$

where $0 \leq p \leq 1$ and $x=0,1,2,...,nt$. With $E(X)=nt*p$ and $Var(X)=nt*p(1-p)$. Given a number of success $x$ and sample size $nt$, the Maximum Likelihood Estimates (MLE) of $Binomial(p)$ is $\hat{p} = x/nt$.

## Parameters:

x (input, int)
The value of the binomial variate. $0 \leq x$
nt (input, int)
Sample size, $nt$ is a positive integer.
p (input, double)
The probability for the incidence to occur, $0 \leq p \leq 1$.
bnp (output, double)
The probability to be calculated.