PDFs of functions of random variables
(2.4 hours to learn)
The PDF of a continuous function of continuous random variables can be computed in terms of the joint PDF and the Jacobian of the function.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
- Section 3.8, "Functions of a random variable," pages 158-164
- Section 3.9, "Functions of two or more random variables," pages 165-175
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
- Section 2.3, "Functions of a random variable," pages 58-63
- Section 3.6, "Functions of jointly distributed random variables," pages 96-104
→ A First Course in Probability
An introductory probability textbook.
- Section 5.7, "The distribution of a function of a random variable," pages 242-244
- Section 6.7, "Joint probability distribution of functions of random variables," pages 300-308
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