= Bernoulli Distribution =

The '''Bernoulli distribution''' is a discrete propability distribution that gives 1 with probability ''p'' and 0 with probability ''q = 1 - p''.

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== Statistics ==

The expected value of a Bernoulli-ditributed variable is ''E[X] = p''.

The variance of a Bernoulli-distributed variable is ''Var[X] = p(1 - p) = pq''.

The sum of repeated and independent Bernoulli-distributed events are described by the [[Statistics/BinomialDistribution|binomial distribution]].

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== Sampling ==

If all frame listings have an equal probability of selection, sampling can be implemented like:

{{{
scalar p = .2 /* Probability of selection */
set seed 123456789
generate double r = runiform()
generate sampled = (r < p)
}}}

The expected number of cases sampled is ''np''; the sample size is described by the [[Statistics/BinomialDistribution|binomial distribution]].



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