3.5.3.7.2 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.