midProbability
What is the law of large numbers?
Updated May 17, 2026
Short answer
It states that sample average converges to expected value as sample size increases.
Deep explanation
The law of large numbers ensures that as the number of trials increases, empirical averages stabilize around theoretical expectation, forming the basis of statistical inference.
Real-world example
Casino outcomes stabilizing over long-term play.
Common mistakes
- Believing short-term outcomes must reflect expectation.
Follow-up questions
- What is weak vs strong LLN?
- Why is LLN important?