Difference between Continuous and Discrete Uniform Distribution

Formula of Continuous and Discrete Uniform Distribution

FAQs on Continous and Discrete Uniform Distribution

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

Basis	Discrete Uniform Distribution	Continuous Distribution
Nature of Outcomes	Finite and countable set of outcomes	Infinite and uncountable range of outcomes
Probability Function	Probability Mass Function (PMF): P(X=x)= 1/n	Probability Density Function (PDF): f(x) = 1/(b-a)
Range of Values	Specific discrete values x₁,x₂,…,x_n	Continuous range of values between a and b
Probability Calculation	Equal probability for each outcome: P(X=x)= 1/n	Equal density across the interval: f(x)= 1/(b-a)
Cumulative Distribution	CDF increases stepwise with each outcome and is defined by F(x) = P(X ≤ x).	CDF is a linear function within the interval defined by F(x) = (x – a) / (b – a) for a ≤ x ≤ b
Support	Specific values within a finite set	Continuous interval [a,b]
Real-World Application	Games of chance, like dice rolls or card draws	Random selection within a time interval, length measurement, etc.
Example	Rolling a fair six-sided die (outcomes: 1, 2, 3, 4, 5, 6)	Selecting a random point on a line segment from 1 to 10

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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.