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A Bernoulli (binary) variable is a random variable that
can take only the value of either
1 (**success**) or 0 (**failure**).
Bernoulli variables are commonly
used for describing binary
processes such as coin tossing, rain/no rain, yes/no decisions etc..
The Bernoulli distribution uses one population parameter
to define the probability of success
and the
probability of failure
.
This can be written more succinctly as

where takes the value of either 0 or 1.
The parameter completely determines the population distribution
and all possible statistics based on , for example, the population
mean is given by
and the population variance is given
by
.
A random variable distributed with a Bernoulli distribution
is described as
by statisticians (the symbol
means ``distributed as'').

David Stephenson
2005-09-30