Binomial Distribution

Binomial Distribution §

def. Binomial Distribution. For random variable $X$ which denotes the number of successes within $n$ trials with success probability $p$:

$$\begin{array}{rl}X& \sim \text{Binom}(n,p)\\ P(X=k)& =\left(\genfrac{}{}{0ex}{}{n}{k}\right)\cdot p^k\cdot (1-p{)}^{n-k}\end{array}$$

• $E[X]=np$
• $Var[X]=n\cdot p(1-p)$