A Holistic Look at Bernoulli Distribution

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.

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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.

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

If you are interested in learning more about probability distributions and related statistical concepts, you should look for Simplilearn's Data Analytics Certification Program. It is one of the most detailed online programs out there for this.  

If you have any questions for us, please mention them in our comments section and we will get back to you.

About the Author

Aryan GuptaAryan Gupta

Aryan is a tech enthusiast who likes to stay updated about trending technologies of today. He is passionate about all things technology, a keen researcher, and writes to inspire. Aside from technology, he is an active football player and a keen enthusiast of the game.

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