What Is The Bernoulli Distribution?

1 Mathematical Statistics- StatIII University of Djilali Liabes - Sidi BelAbbes Discrete Probability Distributions : Bernoulli Distribution The Bernoulli distribution is a discrete probability distribution applicable to experiments involving only two outcomes. It is used to represent binary random variables, which have only two values. The random experiment in this case is known as the Bernoulli trial. Examples of such variables include gender (male or female), binary decisions (yes or no), parity (even or odd), and outcomes like success or failure. The numerical expression of qualitative variables, such as gender (male or female), injury or non-injury, and success or failure, is achieved through coding, we express, for example, the male as (X=1) and the female as (X=0). In the context of the Bernoulli trial, outcomes are classified as either success or failure. Binary notation, with (X=1) representing success and (X=0) representing failure, is used to express these outcomes. This binary representation is a common practice in statistical analysis, particularly when dealing with a series of Bernoulli trials such as the Binomial, geometric, or negative binomial distributions. A discrete random variable X follows a Bernoulli distribution if its probability mass function has the following formula:2 The PMF above takes the values