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.