Uniform Distribution (Discrete)

The discrete uniform distribution has an outcome space over a range of values, each of which happens with equal probability.

$$P(X = x) =\begin{cases}1/(b - a + 1), &x \in \{a, ..., b\}\\0, &x \notin \{a, ..., b\}\end{cases}$$

A real-world system this distribution can model is rolling a fair 6 sided die. Here, a = 1 and b = 6, meaning that the die roll can result in a value from 1 to 6, each with a 1/6 probability of occurring.

Question

Which of the following can be reasonably modeled by the discrete uniform distribution?

(a) A biased coin flip where the probability of heads is less than the probability of tails

(b) Drawing a queen from a standard deck of 52 cards

(c) A raffle where each ticket corresponds to a unique person

Answer