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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
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
A random variable distributed with a Bernoulli distribution
is described as
by statisticians (the symbol
means ``distributed as'').