cumulative distribution function
(1.1 hours to learn)
The cumulative distribution function (CDF) of a random variable X is the function F, where F(a) is the probability that X <= a. CDFs are a convenient representation because they apply to both discrete and continuous random variables, and they can simplify many calculations.
This concept has the prerequisites:
- Know the definition and basic properties of the CDF
- Be able to use the CDF of a distribution to:
- determine the probability that a random variable lies in a given range
- recover the probability mass function or the probability density function
Core resources (read/watch one of the following)
→ A First Course in Probability
An introductory probability textbook.
- Section 4.2, "Discrete random variables," pages 138-140
- Section 4.9, "Properties of the cumulative distribution function," pages 183-184
- Section 5.1, "Introduction," pages 205-209
Supplemental resources (the following are optional, but you may find them useful)
→ Sets, Counting, and Probability
Online lectures on basic probability theory.
Location: Lecture "Random variables"
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 3.3, "The distribution function," pages 109-116
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