## Bernoulli Distribution

The probability mass function of Bernoulli distribution is

`$P(X=x) = p^x q^{1-x}, \; x=0,1; 0<p,q<1; q=1-p.$`

## Mean of Bernoulli Distribution

The mean (expected value) of Bernoulli random variable $X$ is

### $E(X) = p$.

## Variance of Bernoulli Distribution

The variance of Bernoulli random variable $X$ is

### $V(X) = pq$.

## Moment Generating Function of Bernoulli Distribution

The moment generating function (M.G.F.) of Bernoulli distribution is

### $M_X(t) = (q + pe^t)$ for $t\in R$.

## Probability Generating Function of Bernoulli Distribution

The probability generating function (P.G.F.) of Bernoulli distribution is

### $P_X(t) = q+pt$, $t\in R$.

## Characteristic Function of Bernoulli Distribution

The Characteristic function of Bernoulli distribution is