Formula of Continuous and Discrete Uniform Distribution

Below are formulas of continuous and discrete uniform distribution:

Distribution Type

Description

Probability Density Function/ Probability Mass Function

Cumulative Distribution Function

Discrete Uniform

Finite set of equally likely outcomes

P(X=x)= 1/n for x=x1ā€‹,x2ā€‹,ā€¦,xnā€‹

F(x)=Number of outcomes ā‰¤ x/nā€‹

Continuous Uniform

Continuous range of equally likely outcomes between a and b

f(x)= 1ā€‹/(b-a) for a ā‰¤ x ā‰¤ b

F(x)= [Tex]\begin{cases} 0 & \text{if } x < a \\ \frac{x ā€“ a}{b ā€“ a} & \text{if } a \leq x \leq b \\ 1 & \text{if } x > b \end{cases}[/Tex]

Difference between Continuous and Discrete Uniform Distribution

Continuous and discrete uniform distributions are two types of probability distributions. A continuous uniform distribution has an interval of equally likely values. Instead, a discrete uniform distribution applies to a finite set of outcomes with equal probabilities.

In this article, we will discuss continuous and discrete uniform distribution along with a difference between them.

Table of Content

  • What is Continuous Distribution?
  • What is Discrete Uniform Distribution?
  • Formula of Continuous and Discrete Uniform Distribution
  • Difference between Continuous and Discrete Uniform Distribution

Similar Reads

What is Continuous Distribution?

Continuous uniform distribution is a probability distribution in which all outcomes are equally likely within a specified interval [a,b]. In other words, the probability density function (PDF) is constant over this interval, and the distribution is defined by the two parameters a and b, which are the lower and upper bounds, respectively....

What is Discrete Uniform Distribution?

Discrete uniform distribution is a kind of probability distribution in which every possible result has equal likelihood of occurrence. When there are limited possibilities and every one of them is equally likely, this distribution is applied....

Formula of Continuous and Discrete Uniform Distribution

Below are formulas of continuous and discrete uniform distribution:...

Difference between Continuous and Discrete Uniform Distribution

The difference between continuous distribution and discrete uniform distribution can be understood from the table given below....

FAQs on Continous and Discrete Uniform Distribution

Is uniform distribution a continuous distribution?...