Discrete Uniform Distribution

Probability · Axiom Academy

LESSON Discrete Uniform Distribution Equal probability for each outcome in a finite set A random variable X follows a Discrete Uniform distribution if: X takes values in a finite set a, a+1, ..., b Each value has equal probability Common notation: X ~ U a, b or DUnif(a, b) Number of values: n = b - a + 1 The PMF is constant across all values in the support: 3. Expected Value and Variance For a uniform distribution on 1, 2, ..., n : E[X] = (n+1)/2: The mean is at the center Var(X) = (n²-1)/12: Variance grows with range For general a, ..., b : E[X] = (a+b)/2

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