University⏱ 4 min

Law of Large Numbers

Why average approaches expected value

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00.250.50.751p=0.5x̄=0.460
p = 0.50
n = 50
Xˉn→n→∞p=0.5\bar{X}_n \xrightarrow{n\to\infty} p = 0.5

Law of large numbers: the average of n independent observations converges to the true probability p. With larger n, the running average stabilises.