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## A. The Binomial Distribution

This you have seen in CS1021. It is also called a Bernoulli distribution. It is applicable to the situation where there are independent trials, each of which can have one of two outcomes. Call one of the outcomes and the other . Let be the probability that any trial yields the outcome . Then the probability of getting 1's in trials is given by

where

The expected mean number of 1's is ; the variance is

In the limit of large with fixed, a binomial distribution is well approximated by a continuous Gaussian distribution, with the appropriate mean and variance.

Jon Shapiro
1999-09-23