Binopdf
Definition:
bnp = binopdf(x, nt, p) returns the probability density function of the binomial distribution with parameters nt and p.
/math-706dcd4f7b74a1b11a0791892cbe1d6a.png "f(x|nt, p) = \left( \begin{matrix} nt \\ x \end{matrix}\right) p^x (1-p)^{nt-x},")
where /math-8f4ea9a0cdd8693a22df6edd418d412b.png "0 \leq p \leq 1")
and /math-687abe9c170a554ce3f2f5490ebacfbf.png "x=0,1,2,...,nt")
. With /math-19cb657603d2320c25b6104c98808f66.png "E(X)=nt*p")
and /math-e6332b80057c07aa561660b4ae8091c2.png "Var(X)=nt*p(1-p)")
. Given a number of success /math-9dd4e461268c8034f5c8564e155c67a6.png "x")
and sample size /math-25930e3036f13852cb0b29694bbab611.png "nt")
, the Maximum Likelihood Estimates (MLE) of /math-4caf28f44f9d1aac5a8c81c7179cd28a.png "Binomial(p)")
is /math-f31c72066d077a0106f3da5c68143f23.png "\hat{p} = x/nt")
.
Parameters:
- x (input, int)
- The value of the binomial variate.
/math-7eec3b3e7306d5b3210549f4cfc4c81f.png "0 \leq x")
- nt (input, int)
- Sample size, is a positive integer.
- p (input, double)
- The probability for the incidence to occur, .
- bnp (output, double)
- The probability to be calculated.