independent random variables
(1.1 hours to learn)
Intuitively, two random variables are independent if they don't influence each other. Mathematically, two random variables are independent if the events associated with each random variable lying in some set are independent. In statistics and probabilistic modeling, different random variables are often assumed to be independent in order to allow for efficient estimation and inference.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Mathematical Monk: Probability Primer (2011)
Online videos on probability theory.
- expectation and variance
- This uses the measure theoretic notion of probability, but should still be accessible without that background. Refer to Lecture 1.S for unfamiliar terms.
→ A First Course in Probability
An introductory probability textbook.
Location: Section 6.2, "Independent random variables," pages 267-279
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 3.4, "Independent random variables," pages 84-86
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 3.5, "Marginal distributions," subsection "Independent random variables," pages 131-135
Supplemental resources (the following are optional, but you may find them useful)
→ Sets, Counting, and Probability
Online lectures on basic probability theory.
Location: Lecture "Variables"
- We may also want to ask whether two variables are independent conditioned on a third .
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