Binomial Distribution

Binomial Distribution

• A discrete model for $n$ independent Bernoulli trials (success with probability $p$, failure with $1-p$).
• Random variable $X$ = number of successes.
• Probability-mass function (PMF) $$P(X=k)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)p^k(1-p{)}^{n-k},k=0,1,\dots ,n.$$
• Mean and variance $$\mu =np,{\sigma }^2=np(1-p).$$