binomial distribution

二项分布
#probability #statistics

Definition

probability of getting $k$ successes in $n$ independent trials each with same rate $p$

probability mass function

The probability mass function is given by

f(k,n,p) = \Pr[X=k] = {n \choose k} p^k (1-p)^{n-k}

where binomial coefficient for $k=0,1,2,...,n$ is given by

{n \choose k} = \frac{n!}{k! (n-k)!}

Notes

special case when $n=1$ (only one trial) is the Bernoulli distribution

References

https://en.wikipedia.org/wiki/Binomial_distribution