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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*