Binomial equations

· Format:

Binomial(p, n)

· Probability mass function:

$\begin{array}{l}\displaystyle f(x)=\binom{n}{x}p^x(1-p)^{n-x}\end{array}$

· Cumulative distribution function:

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

· 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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