binomial(49, 6); nueberk(49, 6); nCr(49, 6)
5!
5.5!
N=20; r=12; n=10
Probability:
p=r/N; q=1-p
Binomial distribution
// Probability function: (k->P(X=k)=B(k,n,p))
B(k,n,p)=binomial(n,k)*p^k*q^(n-k)
plot( B(k,n,p), k=0..10 )
Expectation:
n*p
Variance:
n*p*q
Hypergeometric distribution:
// Probability function: (k->P(X=k)=Hyp(k,N,r,n))
Hyp(k,N,r,n)=(binomial(r,k)*binomial(N-r,n-k))/binomial( N, n )
plot( Hyp( k, N, r, n ), k=0..10 )
Expectation:
n*p
Variance:
n*p*q*((N-n)/(N-1))
