Which is an example of a discrete uniform distribution?

• A. A biased die roll where outcomes have unequal probabilities.
• B. A fair die roll X ∈ {1,2,3,4,5,6} with P(X=i) = 1/6.
• C. A roll of a die conditioned on previous results.
• D. A continuous uniform distribution on [0,1].

Answer: (B)

Discrete uniform distribution means you have a finite set of outcomes and each one is equally likely. A fair six-faced die has exactly six outcomes: 1 through 6, and if the die is fair, each face occurs with probability 1/6. So a random variable X that takes values in {1, 2, 3, 4, 5, 6} with P(X = i) = 1/6 for i = 1,…,6 is a textbook example of a discrete uniform distribution. The probabilities add up to 1, and every outcome in the set is treated the same way.

The other scenarios don’t fit: a biased die assigns different probabilities to faces, so it isn’t uniform; conditioning on previous results changes the distribution based on history, not a single equal set of probabilities; and a continuous uniform distribution involves any real number in an interval with a constant density, which is not a discrete, finite set of outcomes.