# strong law of large numbers

## Summary

Roughly, the laws of large numbers state that the average of a large number of draws of a random variable approaches the expectation. The strong law states that the probability that the average of the sequence fails to converge to the expectation is zero. This is a strictly stronger statement than the weak law, but requires stronger assumptions.

## Context

This concept has the prerequisites:

- independent random variables (The strong law is a statement about independent random variables.)
- expectation and variance (The strong law is about convergence to an expectation.)
- weak law of large numbers

## Core resources (we're sorry, we haven't finished tracking down resources for this concept yet)

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Mathematical Monk: Probability Primer (2011)

Online videos on probability theory.

## -Paid-

→ A First Course in Probability

An introductory probability textbook.

Location:
Section 8.4, "The strong law of large numbers," pages 443-445

## See also

-No Additional Notes-