In the theory of finite population sampling, Bernoulli sampling is a sampling process where each element of the population

Statistical population

A statistical population is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population. For example, if we were interested in generalizations about crows, then we would describe the set of crows that is of interest...

 that is sampled is subjected to an independent

Statistical independence

In probability theory, to say that two events are independent intuitively means that the occurrence of one event makes it neither more nor less probable that the other occurs...

 Bernoulli trial

Bernoulli trial

In the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure"....

 which determines whether the element becomes part of the sample during the drawing of a single sample. An essential property of Bernoulli sampling is that all elements of the population have equal probability of being included in the sample during the drawing of a single sample.

Bernoulli sampling is therefore a special case of Poisson sampling

Poisson sampling

In the theory of finite population sampling, Poisson sampling is a sampling process where each element of the population that is sampled is subjected to an independent Bernoulli trial which determines whether the element becomes part of the sample during the drawing of a single sample.Each element...

, where each element of the population may have a different probability of being included in the sample.

Because each element of the population is considered separately for the sample, the sample size is not fixed but rather follows a binomial distribution.

Further reading

• Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, ISBN 0-387-40620-4