Bernoulli Distribution

Definition

$X\sim \mathrm{Ber}(p)=B(1,p)$ where $p\in [0,1]$ is a probability of success

number of success in a single trial with success probability $p$

Bernoulli Process

The i.i.d. Random Vector $X_1,\dots ,X_n$ with Bernoulli distribution

Properties

PDF

$f(x)=p^x(1-p{)}^{1-x},x\in \{0,1\}$

Mean

$E(X)=p$

Variance

$\mathrm{Var}(X)=p(1-p)$