Web Reference: Jul 23, 2025 · It is a non-decreasing function that provides a complete description of the distribution of the random variable. For example, if you're looking at the CDF for a test score of 80, and it gives you 0.75, this means there's a 75% chance that a random student's score will be 80 or less. A cumulative distribution function (CDF) describes the probabilities of a random variable having values less than or equal to x. It is a cumulative function because it sums the total likelihood up to that point. Its output always ranges between 0 and 1. CDFs have the following definition: CDF(x) = P(X ≤ x) Where X is the random variable, and x is a... The Kolmogorov–Smirnov test is based on cumulative distribution functions and can be used to test to see whether two empirical distributions are different or whether an empirical distribution is different from an ideal distribution.
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