probability - Proof explanation - weak law of large numbers - Mathematics Stack Exchange

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Let $(X_i)$ be i.i.d. random variables with mean $\mu$ and finite variance. Then $$\dfrac{X_1 + \dots + X_n}{n} \to \mu \text{ weakly }$$ I have the proof here: What I don't understand is, why it

probability - Is the Law of Large Numbers empirically proven? - Mathematics Stack Exchange

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Proof of the Law of Large Numbers Part 1: The Weak Law

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probability - Is the Law of Large Numbers empirically proven? - Mathematics Stack Exchange

Weak Law of Large Numbers (WLLN). Overview, by Pablo Kowalski Kutz

Weak Law of Large Numbers (WLLN). Overview, by Pablo Kowalski Kutz