Student[Statistics]
BernoulliRandomVariable
Bernoulli random variable
Calling Sequence
Parameters
Description
Examples
References
Compatibility
BernoulliRandomVariable(p)
p

probability of success
The Bernoulli random variable is a discrete probability random variable with probability function given by:
$f\left(t\right)=\left\{\begin{array}{cc}1p& t=0\\ p& t=1\\ 0& \mathrm{otherwise}\end{array}\right.$
subject to the following conditions:
$0\le p,p\le 1$
The Bernoulli random variable comes about as a consequence of a single Bernoulli trial. Success of the Bernoulli trial is indicated with x=1 and failure is indicated with x=0, where a success occurs with probability p. The parameter p is also referred to as the Bernoulli probability parameter.
$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Statistics}\right]\right)\:$
$X\u2254\mathrm{BernoulliRandomVariable}\left(p\right)\:$
$\mathrm{ProbabilityFunction}\left(X\,0\right)$
${1}{}{p}$
$\mathrm{ProbabilityFunction}\left(X\,1\right)$
${p}$
$\mathrm{Mean}\left(X\right)$
$\mathrm{Variance}\left(X\right)$
${p}{}\left({1}{}{p}\right)$
$Y\u2254\mathrm{BernoulliRandomVariable}\left(\frac{1}{3}\right)\:$
$\mathrm{ProbabilityFunction}\left(Y\,x\,\mathrm{output}=\mathrm{plot}\right)$
$\mathrm{CDF}\left(Y\,x\right)$
$\left\{\begin{array}{cc}{0}& {x}{<}{0}\\ \frac{{2}}{{3}}& {x}{<}{1}\\ {1}& {\mathrm{otherwise}}\end{array}\right.$
$\mathrm{CDF}\left(Y\,1\,\mathrm{output}=\mathrm{plot}\right)$
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman L.; and Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
The Student[Statistics][BernoulliRandomVariable] command was introduced in Maple 18.
For more information on Maple 18 changes, see Updates in Maple 18.
See Also
Statistics[Distributions][Bernoulli]
Student
Student[Statistics][RandomVariable]
Download Help Document
What kind of issue would you like to report? (Optional)