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Probability density functions that demonstrate the difference between the weak and strong forms of the law of large numbers

score 177 · Answer 1 · 2026-04-11 20:15:08

177

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Probability density functions that demonstrate the difference between the weak and strong forms of the law of large numbers

Published on 11 Apr 2026 - 20:15

score 59 · Answer 2 · 2026-04-16 04:13:08

59

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Show that $\mathbb{P}(\exp(\sum_{i=1}^n X_i) >1)\to\frac{1}{2}$ for $X_i\in L^2$ i.i.d. with zero mean

Published on 16 Apr 2026 - 4:13

score 157 · Answer 3 · 2026-04-13 04:06:13

157

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Proof of a corollary for the Strong Law of Large Number

Published on 13 Apr 2026 - 4:06

score 157 · Answer 4 · 2026-04-14 07:07:19

157

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Law of large numbers without independence and identical distributed assumption

Published on 14 Apr 2026 - 7:07

score 58 · Answer 5 · 2026-04-12 06:10:20

58

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Law of large numbers without any assumption

Published on 12 Apr 2026 - 6:10

score 221 · Answer 6 · 2026-04-11 22:54:34

221

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Some misunderstandings while reading the proof of Berry-Esseen Theorem

Published on 11 Apr 2026 - 22:54

score 101 · Answer 7 · 2026-04-16 19:40:50

101

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A problem with a application of SLLN and CLT and distribution convergence

Published on 16 Apr 2026 - 19:40

score 99 · Answer 8 · 2026-04-13 21:01:26

99

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proof that the sequence satisfies weak law of large numbers

Published on 13 Apr 2026 - 21:01

score 349 · Answer 9 · 2026-04-13 04:06:20

349

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Expected value of mean of N Chi squared random variables

Published on 13 Apr 2026 - 4:06

score 48 · Answer 10 · 2026-05-11 09:32:22

48

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Sum of Independent, Mean Zero, Finite Variance Random Variables

Published on 11 May 2026 - 9:32

score 93 · Answer 11 · 2026-04-17 07:27:14

93

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Law of large numbers for non-stationary but independent process?

Published on 17 Apr 2026 - 7:27

score 52 · Answer 12 · 2026-04-10 16:52:01

52

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Weak Law of Large Numbers Convergence

Published on 10 Apr 2026 - 16:52

score 29 · Answer 13 · 2026-04-12 01:13:00

29

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Growth in $n$ of average $\sum_i X_i/n$ for iid positive $X_i$ with unbounded expectation

Published on 12 Apr 2026 - 1:13

score 131 · Answer 14 · 2026-04-15 20:31:39

For i.i.d. $\{X_n\}$ with non-constant $X_n > 0$ and $\mathbb{E}X_n = q \leq 1$ the product $\prod\limits_{n=1}^{+\infty}X_n \to 0$ almost surely

score 367 · Answer 15 · 2026-04-13 07:48:58

367

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Strong law of large numbers - Continuous martingales - Reference request

Published on 13 Apr 2026 - 7:48

List Question

Probability density functions that demonstrate the difference between the weak and strong forms of the law of large numbers

Show that $\mathbb{P}(\exp(\sum_{i=1}^n X_i) >1)\to\frac{1}{2}$ for $X_i\in L^2$ i.i.d. with zero mean

Proof of a corollary for the Strong Law of Large Number

Law of large numbers without independence and identical distributed assumption

Law of large numbers without any assumption

Some misunderstandings while reading the proof of Berry-Esseen Theorem

A problem with a application of SLLN and CLT and distribution convergence

proof that the sequence satisfies weak law of large numbers

Expected value of mean of N Chi squared random variables

Sum of Independent, Mean Zero, Finite Variance Random Variables

Law of large numbers for non-stationary but independent process?

Weak Law of Large Numbers Convergence

Growth in $n$ of average $\sum_i X_i/n$ for iid positive $X_i$ with unbounded expectation

For i.i.d. $\{X_n\}$ with non-constant $X_n > 0$ and $\mathbb{E}X_n = q \leq 1$ the product $\prod\limits_{n=1}^{+\infty}X_n \to 0$ almost surely

Strong law of large numbers - Continuous martingales - Reference request

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