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Variance of a Bernoulli random variable

Module by: Marco Taboga. E-mail the author

Summary: This module shows how to derive the variance of a Bernoulli random variable.

The variance of the Bernoulli distribution can be easily derived using the variance formula:

Var[X]=E[X^2]-E[X]^2

If you denote by p the probability of success, i.e. the probability that X equals 1, then

E[X]=p*1+(1-p)*0=p

E[X^2]=p*1^2+(1-p)*0^2=p

Therefore:

Var[X]=E[X^2]-E[X]^2=p-p^2=p*(1-p)

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