Law of Large Numbers (LLN)

The Law of Large Numbers (LLN) is a fundamental concept in probability and statistics. It states that as the size of a sample increases, the sample mean (average) will get closer and closer to the expected value (true mean) of the population from which the sample is drawn.

In other words:
If you repeat an experiment a large number of times, the average result will likely be close to the theoretical average. For example, if you flip a fair coin many times, the proportion of heads will get closer to 50% as the number of flips increases.

Key Points:

• Sample Mean Approaches Population Mean: With more data, averages stabilize.
• Two Types:
  • Weak Law of Large Numbers: Convergence in probability.
  • Strong Law of Large Numbers: Almost sure convergence.
• Applications: Gambling, insurance, polling, quality control, and more.

Edit By: Dr. Engineer / Adel Ramadan