Bernoulli Distribution

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


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 binomial distribution.


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 binomial distribution.


CategoryRicottone

Statistics/BernoulliDistribution (last edited 2024-06-14 15:43:35 by DominicRicottone)