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

If is a discrete random variable having support and probability mass function , it is integrable if and only if

This condition, called absolute summability, guarantees that the expected valueis well-defined.

If is a continuous random variable having support and probability density function , it is integrable if and only if

This condition, called absolute integrability, guarantees that the expected valueis well-defined.

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

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

Previous entry: Information matrix

Next entry: Joint distribution function

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.

Featured pages

- Almost sure convergence
- Convergence in distribution
- Bernoulli distribution
- Convergence in probability
- Gamma function
- Permutations

Explore

Main sections

- Mathematical tools
- Fundamentals of probability
- Probability distributions
- Asymptotic theory
- Fundamentals of statistics
- Glossary

About

Glossary entries

Share

- To enhance your privacy,
- we removed the social buttons,
- but
**don't forget to share**.