Binomial variables are frequently encountered in epidemiological data, and the binomial distribution is used to model the prevalence rate and cumulative incidence rate. Binomial variables are created through repeated trials of a Bernoulli process, often called Bernoulli trials. Daniel Bernoulli (1700–1782) was the first mathematician to work out the mathematics for Bernoulli trials. Bernoulli trials must satisfy the following three conditions:

  • The experiment has two possible outcomes, labeled success (S) and failure (F).
  • The trials are independent.
  • The probability of a success remains the same from trial to trial; this is called the success probability and is denoted with the letter p:

The word success as used here is arbitrary and does not necessarily represent something good. Either of the two possible categories may be called ...

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