# Binomial distribution Calculator

## Calculates the probability mass function and lower and upper cumulative distribution functions of the binomial distribution.

percentile x
(success number)
 0≦x≦n
trials n
 n=1,2,...
probability of success p
 0≦p≦1
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Binomial\ distribution\\[10](1)\ probability\ mass\\\hspace{30}f(x,n,p)={}_nC_xp^x(1-p)^{n-x}\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,n,p)={\large\sum_{t=0}^{x}}f(t,n,p)\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,n,p)={\large\sum_{t=x}^{n}}f(t,n,p)\\(4)\ expectation(mean):\hspace{10}np\\$

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