Home page for accesible maths 3.1 Discrete Probability Models 3.1 Discrete Probability Models 3.1.2 Bernoulli Random Variables:

\operatorname{\mathsf{Bern}}(\theta)

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3.1.1 Discrete Uniform Random Variables: ${\operatorname{\mathsf{Unif}}}(0,m)$

A model for outcomes of experiments which involve selecting at random from a sample space $\{0,1,\ldots,m\}$ . Here

\displaystyle p(r;\theta)=\left\{\begin{array}[]{ll}\frac{1}{m+1}&\quad r=0,1,% \ldots,m\\ 0&\quad\text{otherwise}\end{array}\right.

and $p(r;\theta)=0$ otherwise ( $\theta=m$ ), and

$\operatorname{\mathsf{E}}\left[{R}\right]=\frac{m}{2}$ ,
${\operatorname{\mathsf{Var}}}\left[{R}\right]=\frac{m(m+2)}{12}$ .