Binomial Distribution

A discrete Random Variable is of binomial distribution if its range is $\mathbb{N}$ and

• Notation
  • $B(n,p)$
• Parameters
  • $n\in \mathbb{N},p\in [0,1]$
• PMF
  • $p(k)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)p^k(1-p{)}^{n-k}$
• Mean
  • $np$
• Variance
  • $npq$
• MGF
  • $(q+p{e}^t{)}^n$