CDF for Continuous Variables

Probability · Axiom Academy

LESSON CDF for Continuous Variables The cumulative distribution function bridges PDFs and probabilities The cumulative distribution function F(x) gives the probability that the random variable X is less than or equal to x: This is computed by integrating the PDF from negative infinity up to x, accumulating all probability up to that point. Non-decreasing: As x increases, F(x) never decreases (it can stay flat or increase). Bounded: F(x) ranges from 0 to 1, with F(-∞) = 0 and F(∞) = 1. Right-continuous: The CDF is continuous from the right at every point for continuous random variables. The PDF and CDF are intimately related through calculus: CDF from PDF: F(x) is the integral of f(x). PDF from CDF: f(x) is the derivative of F(x).

This is the written version of the interactive lesson above. See the full Probability course.