Home page for accesible maths 3.1 Discrete Probability Models 3.1.1 Discrete Uniform Random Variables:

{\operatorname{\mathsf{Unif}}}(0,m)

3.1.3 Binomial Random Variables:

\operatorname{\mathsf{Bin}}(n,\theta)

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3.1.2 Bernoulli Random Variables: $\operatorname{\mathsf{Bern}}(\theta)$

A model for outcomes of experiments where the sample space is $\{0,1\}$ and the outcomes are not necessarily equi-probable. Here $p(0)=1-\theta$ , $p(1)=\theta$ and $p(r)=0$ otherwise, which can be written as

\displaystyle p(r)=\left\{\begin{array}[]{ll}\theta^{r}(1-\theta)^{1-r}&\quad r% =0,1\\ 0&\quad\text{otherwise}\end{array}\right.

and

$\operatorname{\mathsf{E}}\left[{R}\right]={\color[rgb]{0.76,0.01,0}\theta,}$
${\operatorname{\mathsf{Var}}}\left[{R}\right]={\color[rgb]{0.76,0.01,0}\theta(% 1-\theta).}$