Bernoulli Distribution

A Random Variable is of Bernoulli distribution if its range is $\{0,1\}$.

• Parameters
  • $p\in [0,1]$
• PMF
  • $p(n)=\{\begin{array}{ll}p,& n=1,,\\ q:=1-p,& n=0.\end{array}$
• CDF
  • $F(x)=\{\begin{array}{ll}0,& x<0,\\ q=1-p,& 0\le x\le 1,\\ 1,& x>1.\end{array}$
• Mean
  • $p$
• Variance
  • $pq$
• MGF
  • $q+p{e}^t$

Properties

The sum of $n$ iid Bernoulli random variables follows a Binomial Distribution.