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Last Updated: Mar 27, 2024

Uniform Distribution

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Speaker
Prerita Agarwal
Data Specialist @
23 Jul, 2024 @ 01:30 PM

Introduction

A mathematical function that provides the probabilities of occurrence of various possible outcomes in an experiment is Probability Distribution. It is the possibility/ probability of every possible outcome of an experiment. Let’s understand Probability Distribution with an example, let be a random variable and denote the outcome of a roll of a dice, then the probability distribution of x can be denoted as-

It can be observed that the sum of all P(X) = 1.

Types of Probability Distribution

 Probability distribution is of two types: Discrete and Continuous Probability Distribution.

  1. If the probabilities of the random variable take only a discrete set of values, then the distribution is called a discrete probability distribution. For example, the probability distribution of a random variable denoting the outcome of a roll of dice.
  2. If the probabilities of the random variable take any value between two numbers i.e. a range of values then the distribution is called a continuous probability distribution. For example, the probability distribution of a random variable denoting the temperature throughout the day.

Cumulative Distribution Function

It is the probability that a random variable X will take a value less than or equal to x. For a discrete random variable,
F(x) = P(X<=x) = P(a)

For a continuous random variable,
F(x) = P(X<=x) = f(x)dx 

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Uniform Probability Distribution

A continuous random variable is said to have uniform distribution provided all the values that belong to its support have identical probability density. The Uniform Distribution is a kind of Continuous Probability Distribution. It is also known as Rectangular Distribution. It has a Continuous Random Variable restricted to a finite interval, and its probability function has a constant density over this interval. 

Let x be a continuous random variable, and its support be a finite interval of numbers [a,b]. We say that it has a uniform distribution on the interval if and only if its probability density function f(x) is

       

Expected value or Mean: 

 

Variance:

For the uniform distribution defined over the interval from a to b, the variance equals

 

Standard deviation:

Since standard deviation is the square root of variance, hence,

 

Frequently Asked Questions

What is probability distribution?

A mathematical function that provides the probabilities of occurrence of various possible outcomes in an experiment is Probability Distribution. It is the possibility/ probability of every possible outcome of an experiment. 

What are the types of probability distributions?

There are two types of Probability Distribution: Discrete and Continuous Probability Distribution. If the probabilities of the random variable take only a discrete set of values, then the distribution is called a discrete probability distribution. If the probabilities of the random variable take any value between two numbers i.e. a range of values then the distribution is called a continuous probability distribution.

What is uniform distribution?

Uniform distributions are continuous probability distributions with equally likely outcomes. It is also known as Rectangular Distribution. It has a Continuous Random Variable restricted to a finite interval, and its probability function has a constant density over this interval. 

Conclusion

In this article, we have extensively discussed Probability Distribution, its types and uniform distribution. We hope that this blog has helped you enhance your knowledge, and if you wish to learn more, check out our  Coding Ninjas Blog site and visit our Library. Do upvote our blog to help other ninjas grow.

Happy Learning! 

Topics covered
1.
Introduction
2.
Types of Probability Distribution
2.1.
Cumulative Distribution Function
3.
Uniform Probability Distribution
4.
Expected value or Mean: 
5.
Variance:
6.
Standard deviation:
7.
Frequently Asked Questions
7.1.
What is probability distribution?
7.2.
What are the types of probability distributions?
7.3.
What is uniform distribution?
8.
Conclusion