Question

Application of the Weak Law of Large Numbers

score 969 · Answer 1 · 2026-04-10 22:57:02

969

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Application of the Weak Law of Large Numbers

Published on 10 Apr 2026 - 22:57

score 34.9k · Answer 2 · 2026-04-09 05:54:34

34.9k

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What is the difference between the weak and strong law of large numbers?

Published on 09 Apr 2026 - 5:54

score 560 · Answer 3 · 2026-04-14 14:52:29

560

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Generalization of Law of Large Numbers and Central Limit Theorem using Polynomial Scaling

Published on 14 Apr 2026 - 14:52

score 141 · Answer 4 · 2026-04-11 14:47:03

141

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Applying Law of Large Numbers to Find Almost Sure Limit

Published on 11 Apr 2026 - 14:47

score 368 · Answer 5 · 2026-04-12 07:49:29

368

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Weighted Sum of Independent Random Variables

Published on 12 Apr 2026 - 7:49

score 76 · Answer 6 · 2026-04-15 04:17:50

76

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Asymptotics of arg max estimator

Published on 15 Apr 2026 - 4:17

score 462 · Answer 7 · 2026-04-17 02:20:47

462

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If $\{X_n\}$ is an i.i.d. sequence of integrable random variables and $S_n=\sum_{i=1}^n X_i$, then $E[X_1|S_n,S_{n+1},\ldots]=\frac{S_n}{n}$.

Published on 17 Apr 2026 - 2:20

score 295 · Answer 8 · 2026-04-13 16:16:38

295

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Limiting Distribution with Finite 4th Moment

Published on 13 Apr 2026 - 16:16

score 175 · Answer 9 · 2026-04-16 02:30:28

175

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If independent centered $X_n$ obeys the weak law of large numbers, then the sequence $n^{-1}X_n$ converges in probability to $0$.

Published on 16 Apr 2026 - 2:30

score 1.2k · Answer 10 · 2026-04-12 05:43:42

1.2k

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Law of large numbers; Poisson distribution

Published on 12 Apr 2026 - 5:43

score 336 · Answer 11 · 2026-04-15 06:43:03

336

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Law of large numbers with random index

Published on 15 Apr 2026 - 6:43

score 57 · Answer 12 · 2026-04-17 03:03:48

57

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$\sum_{j=0}^\infty Z_t^2 Z_{t-1}^2 \ldots Z^2_{t-j} < \infty$ a.s.

Published on 17 Apr 2026 - 3:03

score 1.9k · Answer 13 · 2026-04-12 13:06:43

1.9k

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How to show that $ \hat{\sigma} $ is a consistent estimator of $\sigma $ using the law of large numbers?

Published on 12 Apr 2026 - 13:06

score 111 · Answer 14 · 2026-04-15 00:08:27

111

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Using central limit theorem to prove most of an n dimensional cube is contained in a given annulus

Published on 15 Apr 2026 - 0:08

score 81 · Answer 15 · 2026-04-16 22:29:58

81

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Limit of $E\left(\frac{X_1+\ldots+X_n}{\vert X_1\vert + \ldots + \vert X_n\vert}\right)$ for $(X_k)$ i.i.d. with $P(X_1=0)=0$

Published on 16 Apr 2026 - 22:29

List Question

Application of the Weak Law of Large Numbers

What is the difference between the weak and strong law of large numbers?

Generalization of Law of Large Numbers and Central Limit Theorem using Polynomial Scaling

Applying Law of Large Numbers to Find Almost Sure Limit

Weighted Sum of Independent Random Variables

Asymptotics of arg max estimator

If $\{X_n\}$ is an i.i.d. sequence of integrable random variables and $S_n=\sum_{i=1}^n X_i$, then $E[X_1|S_n,S_{n+1},\ldots]=\frac{S_n}{n}$.

Limiting Distribution with Finite 4th Moment

If independent centered $X_n$ obeys the weak law of large numbers, then the sequence $n^{-1}X_n$ converges in probability to $0$.

Law of large numbers; Poisson distribution

Law of large numbers with random index

$\sum_{j=0}^\infty Z_t^2 Z_{t-1}^2 \ldots Z^2_{t-j} < \infty$ a.s.

How to show that $ \hat{\sigma} $ is a consistent estimator of $\sigma $ using the law of large numbers?

Using central limit theorem to prove most of an n dimensional cube is contained in a given annulus

Limit of $E\left(\frac{X_1+\ldots+X_n}{\vert X_1\vert + \ldots + \vert X_n\vert}\right)$ for $(X_k)$ i.i.d. with $P(X_1=0)=0$

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