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·       Format:

Binomial(p, n)

·       Probability mass function:

f(x)=\binom{n}{x}p^x(1-p)^{n-x}

·       Cumulative distribution function:

F(x)=\displaystyle\sum_{i=0}^{\lfloor x \rfloor} \binom{n}{i}p^i(1-p)^{n-i}

·       Parameter restrictions:

0 < p < 1; n = {0,1,2,...}

·       Domain: 

x = {0,1,2,...n}

·       Mean:

np

·       Mode: 

p (n + 1)-1 and p (n+1)          if p (n+1) is an integer

p (n + 1)                                  otherwise 

·       Variance:

np (1- p)




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