Bernoulli distributions

The Bernoulli distribution is a simple discrete distribution that describes the probability of binary outcomes in an experiment. There are many examples of Bernoulli distributions in our daily lives. Let’s see some real-world examples:

• What is the chance of a student passing an exam?
• What is the chance of a team winning a championship?
• What is the probability of getting an even number when a fair dice is thrown once?

All these cases have one event or one trial – either “yes” or “no,” or “pass” or “fail.” Let’s see its formal definition.

The formal definition of a Bernoulli distribution

A discrete distribution has two possible outcomes:

P(X = x) = { p if x = 1  q = 1 − p if x = 0

This relationship is commonly expressed in an exponential form:

P(x) = p x (1 − p) 1−x for x ∈ (1,0) ...