Scilab Function

binomial - binomial distribution probabilities

### Calling Sequence

  `pr=binomial(p,n)`

### Parameters

- `pr` : row vector with n+1 components
- `p` : real number in [0,1]
- `n` : an integer >= 1

### Description

`pr=binomial(p,n)` returns the binomial probability vector, i.e. `pr(k+1)` is the probability of `k` success in `n` independent Bernouilli trials with probability of success `p`. In other words : pr(k+1) = probability(X=k) , with X a random variable following the B(n,p) distribution, and numerically :

                / n \  k      n-k       / n \       n!
     pr(k+1) =  |   | p  (1-p)    with  |   |  = ---------
                \ k /                   \ k /    k! (n-k)!

### Examples

    // first example
    n=10;p=0.3; xbasc(); plot2d3(0:n,binomial(p,n));

    // second example
    n=50;p=0.4;
    mea=n*p; sigma=sqrt(n*p*(1-p));
    x=( (0:n)-mea )/sigma;
    xbasc()
    plot2d(x, sigma*binomial(p,n));
    deff('y=Gauss(x)','y=1/sqrt(2*%pi)*exp(-(x.^2)/2)')
    plot2d(x, Gauss(x), style=2);

### See Also

`cdfbin` `grand`