Search for probability and statistics terms on Statlect
StatLect

Integrable random variable

by , PhD

A random variable is said to be integrable if its expected value exists and it is well-defined.

Table of Contents

Integrability for discrete variables

If X is a discrete random variable having support R_X and probability mass function [eq1], it is integrable if and only if[eq2]

This condition, called absolute summability, guarantees that the expected value[eq3]is well-defined.

Integrability for continuous variables

If X is a continuous random variable having support R_X and probability density function [eq4], it is integrable if and only if[eq5]

This condition, called absolute integrability, guarantees that the expected value[eq6]is well-defined.

Square integrability

A random variable is said to be square integrable if the expected value of its square exists and it is well-defined.

More details

The lectures entitled Expected value and Variance explain these terms in more detail.

Keep reading the glossary

Previous entry: Information matrix

Next entry: Joint distribution function

How to cite

Please cite as:

Taboga, Marco (2021). "Integrable random variable", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/integrable-random-variable.

The books

Most of the learning materials found on this website are now available in a traditional textbook format.