Law of Large Numbers
=
→
Tap a term to see what it means, or .
Calculate
Example: a fair die has an expected value of 3.5. Rolling it 1,000 times, does the mean of the outcomes get close to that? And in the first rolls? Change the experiment, the number of throws, or draw again.
Step by step
What each term means
- Sample Mean (X̄ₙ)
- The mean of the first n outcomes. It is a random variable: another draw would give another mean, but less and less different as n grows.
- Sum of the Outcomes
- The n independent outcomes of the same experiment, added up. Each has expected value μ and the same variability.
- Number of Repetitions (n)
- How many times the experiment was repeated. The typical distance between X̄ₙ and μ shrinks like 1/√n: four times as many throws, half the error.
- Expected Value (μ)
- The value the mean converges to as n goes to infinity: 3.5 for a fair die, 0.5 for the share of heads of a coin.