Discrete Probability Distributions

Explanation

A discrete uniform distribution assigns equal probability to each value in a finite range. The probability mass function is $P(X = k) = \frac{1}{b - a + 1}$ for $a \leq k \leq b$. The expected value is $E[X] = \frac{a + b}{2}$, and the variance is $\text{Var}(X) = \frac{n^2 - 1}{12}$, where $n = b - a + 1$. Common examples include rolling a fair die, selecting a random card from a deck, or generating a random number from a finite range.