Bernoulli Distribution

A Bernoulli random variable of parameter $p$ takes one of only two values $X=0$ or $X=1$ . The probability of success ( $X=1$ ) is $p$ , and the probability of failure ( $X=0$ ) is $1-p.$ It can be thought of as a binomial random variable with $n=1$ . The PMF is $p\left(k\right)=0$ for $k\ne 0,1$ and