Bernoulli Distribution

All cases in which manifestations have exactly two characteristics follow a Bernoulli distribution.

Typical examples are coin flip or medical treatment, which works or not.

Let X be a random variable with x \in {0,1} and a probability function of



Written in a compact way:

f(x)=\left\{\begin{array}{ll} \pi^{x}(1-\pi)^{1-x} & x\in {0,1} \\ 0 & otherwise\end{array}\right. .

The expected value is defined through:


In case of having a series of Bernoulli events, we are having a Binomial distribution. For example, the out come of a repeated coin flip follows a Binomial distribution.


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