List questions from law-of-large-numbers

Published on 24 Jun 2014 - 3:58

112

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Strange identity in the proof of the Strong Law of Large Numbers

Published on 29 Jun 2014 - 19:38

532

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If $X_{i}$ are I.I.D and $n^{-1}\sum_{i=1}^{n}X_{i}$ converges a.s/in-distribution to a constant $a$ is it true that $a=\mathbb{E}[X_{i}] $?

Published on 30 Jun 2014 - 20:15

123

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Showing $\sum_{k\ge 0} e^{-an} \frac{(an)^k}{k!}f(\frac{k}{n}) = \Bbb{E}\left(f\left(\frac{X_1+\cdots + X_n}{n}\right)\right)$

Published on 27 Mar 2026 - 4:35

2k

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Central Limit Theorem vs. Weak Law of Large Numbers

Published on 07 Aug 2014 - 16:57

73

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Is the law of large numbers reflected in SO reputation system?

Published on 16 Aug 2014 - 10:29

67

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Using Taylors to show convergence in probability

Published on 18 Aug 2014 - 23:07

121

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Moving Limit within Probability/Law of Large Numbers

Published on 24 Aug 2014 - 18:27

181

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Almost sure limit of $\log(X_1 + X_2 + ... + X_n) - \log(n)$

Published on 02 Sep 2014 - 8:34

176

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A LLN type theorem on the supremum of functions of a RV

Published on 26 Mar 2026 - 7:59

1.3k

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Convergence in probability and convergence of Cesaro means

Published on 14 Sep 2014 - 18:39

338

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Almost Sure Convergence for Sample Mean of Bernoullis

Published on 26 Mar 2026 - 4:32

231

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About strong law of large numbers

Published on 07 Oct 2014 - 4:24

5.9k

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Gambler's fallacy and the Law of large numbers

Published on 25 Mar 2026 - 9:50

284

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General Weak Law of Large numbers

Published on 15 Oct 2014 - 4:42

List Question

Betting: Gambler's Fallacy vs. Law of Large Numbers

Strange identity in the proof of the Strong Law of Large Numbers

If $X_{i}$ are I.I.D and $n^{-1}\sum_{i=1}^{n}X_{i}$ converges a.s/in-distribution to a constant $a$ is it true that $a=\mathbb{E}[X_{i}] $?

Showing $\sum_{k\ge 0} e^{-an} \frac{(an)^k}{k!}f(\frac{k}{n}) = \Bbb{E}\left(f\left(\frac{X_1+\cdots + X_n}{n}\right)\right)$

Central Limit Theorem vs. Weak Law of Large Numbers

Is the law of large numbers reflected in SO reputation system?

Using Taylors to show convergence in probability

Moving Limit within Probability/Law of Large Numbers

Almost sure limit of $\log(X_1 + X_2 + ... + X_n) - \log(n)$

A LLN type theorem on the supremum of functions of a RV

Convergence in probability and convergence of Cesaro means

Almost Sure Convergence for Sample Mean of Bernoullis

About strong law of large numbers

Gambler's fallacy and the Law of large numbers

General Weak Law of Large numbers

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