## Binomial distribution

The probability of binomial distribution, in which the probability of a single trial of event is the $p$ and events occurs $x$ times in n trials, is given by the following equation.

$p(x)=\left( \begin{array}{c} n \\ x \\ \end{array} \right)p^x (1-p)^{n-x} , 0\leq x\leq n$

where,

$\left( \begin{array}{c} n \\ x \\ \end{array} \right)=\frac{n!}{x! (n-k)!}$

Binomial distribution random numbers can be obtained by standard exponential distribution random number sequence $E_1, E_2,\cdots$. Maximum of $N$ satisfying the following formula is binomially distributed.

$\sum _{i=1}^N \frac{E_i}{m-i+1}\leq -\log (1-p)$

Reference:
• M.Fushimi, Random number, UP Sensho Applied Mathematics, University of Tokyo Press, 1989

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