Continuous Uniform Distribution

Probability · Axiom Academy

LESSON Continuous Uniform Distribution The simplest continuous distribution with constant probability density over an interval 1. Probability Density Function For a continuous uniform distribution on the interval [a, b], the probability density function is constant across the entire interval. This makes it the simplest continuous distribution. Since the total area under the curve must equal 1, the height is 1/(b-a). The PDF is zero outside [a, b]. 2. Cumulative Distribution Function The CDF increases linearly from 0 to 1 over the interval [a, b]. This linear growth reflects the constant probability density. 3. Expected Value and Variance The expected value is simply the midpoint of the interval. The variance measures the spread of the distribution and depends on the square of the interval length.

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