# PDFs of functions of random variables

(2.4 hours to learn)

## Summary

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.

## Context

This concept has the prerequisites:

- random variables
- multivariate distributions
- determinant (The formula for the PDF of the function involves a determinant.)
- linear approximation (The formula for the PDF of the function involves the partial derivatives of the function.)

## Core resources (read/watch one of the following)

## -Paid-

→ 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

## See also

-No Additional Notes-