Distribution is a key concept in data analytics, data science, and machine learning. It serves as the foundation for statistical analysis of a dataset and the foundation for some machine learning models. In this tutorial, you will look at one such distribution, Bernoulli Distribution.

## Random Variables

Random variables are those whose values depend on the outcomes of an experiment. There are two types of random variables - Discrete and Continuous.

Assume the experiment of rolling a die. Any number between 1 and 6 could be the possible outcome of this experiment. If X is the random variable that denotes the outcome of a random process, the sample space for this experiment will be {1, 2, 3, · · ·, 6}.

## Probability Distribution

A probability distribution is a summary of probabilities for the values of a random variable. It is characterized by a probability density function or probability mass function for continuous or discrete variables.

## What Is Bernoulli Distribution?

The Bernoulli distribution is a discrete probability distribution, which means that it only considers discrete random variables. The number of heads obtained when tossing three coins at once, or the number of students in a class, are examples of discrete random variables with a finite or countable number of possible values.

Bernoulli distribution is a discrete distribution in which the random variable has only two possible outcomes and a single trial known as a Bernoulli trial.

p is the expected value of the Bernoulli random variable, which is known as the Bernoulli distribution parameter.

The experiment's outcome can have only two values i.e, 0 or 1.

Here x is the discrete random variable that can take only one value.

## Examples of Bernoulli Distributions

Although the coin-toss example is simple, there are many situations in life that have a yes-no outcome. Consider the following scenario:

- Will a student pass or fail a test?
- Will India win or lose the match?
- Chances of your job application getting accepted or rejected?

## Conditions of Bernoulli Distribution

There are certain prerequisite conditions associated with Bernoulli distribution:

- There should be only two possible outcomes of your trial.
- Each of the two outcomes should have a fixed probability of occurrence.
- The trials should be independent of each other.

If these conditions are met, it can be considered a Bernoulli trial.

## Application of Bernoulli Distribution

In real-life situations, it's necessary to keep track of whether a specific event occurs. The outcome of such events is recorded as a success or failure. Some places where Bernoulli distribution can be used are:

- The success or failure of a medical treatment
- Transmission or non-transmission of a disease
- A newborn child is male or female

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## Conclusion

In this tutorial, you covered Bernoulli distribution. It is a discrete probability distribution that determines the success or failure of a Bernoulli trial.

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