The Uniform distribution is a continuous random variable where all values between $a$ and $b$ are equally likely. ## Notation $X\sim U[a,b]$ Square brackets are used to denote the interval is inclusive of $a$ and $b$. ## Probability Density Function $f(x) = \frac{1}{b-a}$ ## Expectation $E(X) = \frac{b + a} {2}$ ## Variance $V(X) = \frac{(b - a)^2}{12}$