# Negative binomial distribution Calculator

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

 number of failures before k successes x x=0,1,2,.. number of successes k k=1,2,.. probability of success p 0≦p≦1
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Negative\ Binomial\ distribution\\[10](1)\ probability\ mass\\\hspace{30}f(x,k,p)={}_{x+k-1}C_xp^k(1-p)^x\\(2)\ lower\ cumulative\ distribution\\\hspace{30}P(x,k,p)={\large\sum_{t=0}^{x}}f(t,k,p)\\(3)\ upper\ cumulative\ distribution\\\hspace{30}Q(x,k,p)={\large\sum_{t=x}^{n}}f(t,k,p)\\(4)\ expectation(mean):\hspace{10}k{\large\frac{1-p}{p}}\\$

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