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A discrete Probability Distribution Function is a function that includes some discrete values in its domain. The number of values it includes could be both finite and infinite. It is in no way necessary that these Discrete Probability Distribution Functions may be grouped under the domain of integers but generally this is what is done. These discrete probability distribution functions have values that occur between 0 and 1. If, for example, there exists in nature a discrete probability distribution function that allows you to have values below 0 and values above 1, then that discrete probability distribution function will not be considered a probability function because we already know that the value of probability can only between 0 and 1. 

Types of Probability Distribution Functions

There are two types of Probability Distribution Functions which are respectively Continuous Probability Distribution Function and Discrete Probability Distribution Function.

Continuous Probability Distribution Function: – A Continuous Probability Distribution Function is a Probability Distribution Function that can have any value possible in this mathematical world. This basically means that there is no constraint on the value of the Continuous Probability Distribution Function. An Example of The Continuous Probability Distribution Function may be assumed as the heights of students in a particular class of a school.

Discrete Probability Distribution Function: – A Discrete Probability Distribution Function as we already have seen is a probability distribution function that consists of values that are discrete or dissimilar in nature. That basically means that there is a constraint on the values of a Discrete Probability Distribution Function. An Example of The Discrete Probability Distribution Function may be assumed as the Bernoulli Function.

Cumulative Probability Distribution Function

The Cumulative Probability Distribution Function is defined as a Probability Distribution Function that provides us with the probability of an event that may be less than or equal to some values of that particular Random Variable. The Cumulative Probability Distribution Function is used to determine the sum of probabilities of a particular function up to a particular point. The use of The Cumulative Probability Distribution Function is in determining the p-values. These p-values are very essential in performing Hypothesis Testing. Now we shall see the different types of Discrete Probability Distribution Functions.

Types of Discrete Probability Distribution Functions

  1. Bernoulli Distribution: – Bernoulli Distribution is a type of The Discrete Probability Distribution Function. In The Bernoulli Distribution, the distribution arises upon the completion of a particular experiment. It is given that this particular experiment has only two possible outcomes. These two outcomes of that experiment can be described as success and failure. So to describe in as few words as possible, we can define The Bernoulli Discrete Probability Distribution Function as a Probability Distribution Function in which the distribution arises from the conduction of a particular experiment for which there are only two results possible. The two results possible are success and failure. An example of The Bernoulli Discrete Probability Distribution Function can be assumed as the Flipping of a Coin.
  2. Binomial Distribution: – The Binomial Discrete Probability Distribution Function is a Probability Distribution Function that much like The Bernoulli Discrete Probability Distribution Function consists of only two outcomes which are success and failure. The example for The Binomial Discrete Probability Distribution Function may be thought of as the same as the one for The Bernoulli Distribution that is Flipping a Coin.
  3. Hypergeometric Distribution: – The Hypergeometric Discrete Probability Distribution Function may be described as a Probability Distribution Function that provides the outcomes for a particular number of successes let’s say a for every particular number of experiments conducted let’s say b. That basically means that The Hypergeometric Discrete Probability Distribution Function accounts for the probabilities of successes for every b experiment or trial conducted. 
  4. Negative Binomial Distribution: – The Negative Binomial Discrete Probability Distribution Function is useful when we already know the desired outcome beforehand and we have to just keep on doing the experiments or trials till we come across it. So basically, The Negative Binomial Discrete Probability Distribution Function is used to determine the number of times a particular experiment has to be conducted before we get the desired outcome.
  5. Geometric Distribution: – The Geometric Discrete Probability Distribution Function is a Probability Distribution Function that is a special case of the Negative Binomial Discrete Probability Distribution Function. In This Probability Distribution Function, we have to determine how many failures we can encounter before finally finding one success.

Conclusion

In this article, we learned how to define a Discrete Probability Distribution Function. We have discussed the discrete probability distribution function in detail. Then we saw the two types of Probability Distribution Functions. The two types of Probability Distribution Functions are Continuous Probability Distribution Function and Discrete Probability Distribution Function. Then we looked at The Cumulative Probability Distribution. Finally, we looked at the different types of Discrete Probability Distribution Functions. These are Bernoulli Distribution, Binomial Distribution, Hypergeometric Distribution, Negative Binomial Distribution, and Geometric Distribution.