Key Concepts

• A uniform distribution is a type of continuous random variable, where all outcomes are equally likely on a given range of values.
• Areas of rectangles are used to calculate probabilities associated with uniform distributions.

Glossary

uniform distribution a continuous random variable (RV) that has equally likely outcomes over the domain, [latex]a<x<b[/latex]. Notation: [latex]X \sim U(a,b)[/latex]. The mean is [latex]\mu = \frac{a+b}{2}[/latex] and the standard deviation is [latex]\sigma = \sqrt{\frac{(b-a)^{2}}{12}}[/latex]. The probability density function is [latex]f(x)=\frac{1}{b-a}[/latex] for [latex]a<x<b[/latex] or [latex]a \leq x \leq b[/latex]. The cumulative distribution is [latex]P(X \leq x) = \frac{x-a}{b-a}[/latex].