In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample. An essential property of Bernoulli sampling is that all elements of the population have equal probability of being included in the sample.[1]
Bernoulli sampling is therefore a special case of Poisson sampling. In Poisson sampling each element of the population may have a different probability of being included in the sample. In Bernoulli sampling, the probability is equal for all the elements.
Because each element of the population is considered separately for the sample, the sample size is not fixed but rather follows a binomial distribution.
^Carl-Erik Sarndal; Bengt Swensson; Jan Wretman (1992). Model Assisted Survey Sampling. ISBN 978-0-387-97528-3.
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