Uniform Distribution
All values equally likely.
Key idea
All values equally likely.
In depth
All outcomes (or all values in an interval [a, b]) are equally likely. For continuous uniform, density 1/(b − a), mean (a + b)/2, variance (b − a)²/12.
Worked example
A random number in [0, 10]: P(X < 3) = 3/10, mean 5.
Formula
Real-world uses
- Modelling a fair random number generator or a bus arriving at any time within a 10-minute window
Common mistake
Applying it when the outcomes are not actually equally likely.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Uniform Distribution?
All values equally likely. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Uniform Distribution?
The key formula is f(x) = 1/(b−a).
Where is Uniform Distribution used in real life?
Real-world examples: Modelling a fair random number generator or a bus arriving at any time within a 10-minute window.
What should I learn before Uniform Distribution?
Make sure you are comfortable with Hypergeometric Distribution, the previous topic in Probability & Statistics.
What is a common mistake with Uniform Distribution?
Applying it when the outcomes are not actually equally likely.
How can I practise Uniform Distribution?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Uniform Distribution?
Move on to Normal Distribution next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.