Law of large numbers

Definition

The Law of Large Numbers states that as the number of trials or observations increases, the average of the results becomes closer to the expected value. This principle is fundamental in probability and statistics.

5 Must Know Facts For Your Next Test

1. There are two forms of the Law of Large Numbers: Weak and Strong.
2. The Weak Law of Large Numbers ensures convergence in probability.
3. The Strong Law of Large Numbers ensures almost sure convergence.
4. It underpins many statistical methods, including sampling and estimation.
5. This law justifies the assumption that sample averages will resemble population averages with sufficiently large sample sizes.

Review Questions

• What are the two forms of the Law of Large Numbers?
• How does the Law of Large Numbers justify sampling in statistics?
• What is the difference between weak and strong versions of this law?

Related terms

Central Limit Theorem:

A statistical theory stating that when an infinite number of successive random samples are taken from a population, the distribution of sample means will become approximately normally distributed.

Expected Value:

The long-run average value of repetitions of an experiment it represents.

Convergence in Probability: \(An event's probability approaches one as the number \(n\) increases; often used in context with Weak Law of Large Numbers.\)