Integrable random variable

by Marco Taboga, PhD

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

Integrability for discrete variables

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.

Integrability for continuous variables

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.

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

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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.