Parameters

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