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The Binomial distribution models the number of successes from n independent trials where there is a probability p of success in each trial (as explained in the section on the Binomial process).

The binomial distribution has an enormous number of uses. Beyond simple binomial processes, many other stochastic processes can be usefully reduced to a binomial process to resolve problems. For example:

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Another example: the number of faulty computer chips in a 2000 volume batch where there is a 2% probability that any one chip is faulty = Binomial (2%,2000).

The Binomial distribution was first discussed by Bernoulli (1713). It is related to the Beta and Negative Binomial distributions, all of which have their basis in the Binomial process where the Binomial distribution is also derived. The Bernoulli distribution is a special case of the Binomial with n = 1 i.e.: Bernoulli(p) = Binomial(p,1) that is used to model risk events.

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