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
