study guides for every class

that actually explain what's on your next test

Law of large numbers

from class:

Intro to Statistics

Definition

The Law of Large Numbers states that as the sample size increases, the sample mean will get closer to the population mean. This principle is fundamental in probability and statistics.

congrats on reading the definition of law of large numbers. now let's actually learn it.

ok, let's learn stuff

5 Must Know Facts For Your Next Test

  1. The Law of Large Numbers applies only when samples are independent and identically distributed (i.i.d).
  2. There are two forms: Weak Law of Large Numbers and Strong Law of Large Numbers.
  3. This law helps justify the use of sample data to make inferences about a population.
  4. In practical applications, larger sample sizes typically yield more accurate estimates.
  5. The Central Limit Theorem relies on the principles outlined by the Law of Large Numbers.

Review Questions

  • What conditions must be met for the Law of Large Numbers to apply?
  • How does the Law of Large Numbers relate to the Central Limit Theorem?
  • Explain the difference between the Weak and Strong forms of the Law of Large Numbers.

"Law of large numbers" also found in:

Subjects (63)

© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides