Question

estimating the sum of Cauchy variables by its biggest terms

score 66 · Answer 1 · 2026-03-25 05:15:40

66

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estimating the sum of Cauchy variables by its biggest terms

Published on 25 Mar 2026 - 5:15

score 29 · Answer 2 · 2026-03-25 00:30:13

29

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Showing that inequality holds with high probabilty

Published on 25 Mar 2026 - 0:30

score 316 · Answer 3 · 2026-03-24 18:13:12

316

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Find the limiting probability...

Published on 24 Mar 2026 - 18:13

score 278 · Answer 4 · 2026-03-24 20:04:03

278

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A probability inequality: probability that the normalized sum of i.i.d. random variables is bounded below, is bounded below

Published on 24 Mar 2026 - 20:04

score 289 · Answer 5 · 2026-03-24 03:51:08

289

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Let $P(X_j=j)=P(X_j=-j)=1/2j^{\beta}$ and $P(X_j=0)=1-j^{-\beta}$ where $\beta\in(0,1)$, then $S_n/n^{(3-\beta)/2)}\Rightarrow c\chi$

Published on 24 Mar 2026 - 3:51

score 101 · Answer 6 · 2026-03-23 22:31:23

101

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Does weak convergence imply time average convergence?

Published on 23 Mar 2026 - 22:31

score 511 · Answer 7 · 2026-03-24 18:55:37

511

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What is the rate of growth of $M_n := \max_{1 \le i \le n} U_i^{(n)}$, where $U_i^{(n)} \sim \operatorname{Uniform}[0,n]$? Is it "constant"?

Published on 24 Mar 2026 - 18:55

score 172 · Answer 8 · 2026-03-25 05:43:02

172

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How can we show that this transformation of the cumulative distribution function of the standard normal distribution is bounded?

Published on 25 Mar 2026 - 5:43

score 98 · Answer 9 · 2026-03-24 22:44:19

98

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Show that $n \mathbb{P}\{|X_1| \geq \epsilon \sqrt{n}\} \to 0$

Published on 24 Mar 2026 - 22:44

score 23 · Answer 10 · 2026-03-25 01:58:21

23

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Does this converge in distribution in this case?

Published on 25 Mar 2026 - 1:58

score 209 · Answer 11 · 2026-03-25 04:18:54

209

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Probability limits of random variable sums

Published on 25 Mar 2026 - 4:18

score 272 · Answer 12 · 2026-03-24 17:19:32

272

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Limiting a sequence of moment generating functions

Published on 24 Mar 2026 - 17:19

score 47 · Answer 13 · 2026-03-25 07:47:02

$\lim_{x\rightarrow+\infty} x^{\alpha+\beta}P(|X|>x)=0\Leftrightarrow\lim_{x\rightarrow+\infty}x^{\alpha}E||X|^{\beta}\cdot1_{\{|X|>x\}}|=0$

score 198 · Answer 14 · 2026-03-25 00:18:02

198

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How to prove that the following estimators are biased and consistent?

Published on 25 Mar 2026 - 0:18

score 50 · Answer 15 · 2026-03-24 14:18:53

50

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CLT for decaying random variables

Published on 24 Mar 2026 - 14:18

List Question

estimating the sum of Cauchy variables by its biggest terms

Showing that inequality holds with high probabilty

Find the limiting probability...

A probability inequality: probability that the normalized sum of i.i.d. random variables is bounded below, is bounded below

Let $P(X_j=j)=P(X_j=-j)=1/2j^{\beta}$ and $P(X_j=0)=1-j^{-\beta}$ where $\beta\in(0,1)$, then $S_n/n^{(3-\beta)/2)}\Rightarrow c\chi$

Does weak convergence imply time average convergence?

What is the rate of growth of $M_n := \max_{1 \le i \le n} U_i^{(n)}$, where $U_i^{(n)} \sim \operatorname{Uniform}[0,n]$? Is it "constant"?

How can we show that this transformation of the cumulative distribution function of the standard normal distribution is bounded?

Show that $n \mathbb{P}\{|X_1| \geq \epsilon \sqrt{n}\} \to 0$

Does this converge in distribution in this case?

Probability limits of random variable sums

Limiting a sequence of moment generating functions

$\lim_{x\rightarrow+\infty} x^{\alpha+\beta}P(|X|>x)=0\Leftrightarrow\lim_{x\rightarrow+\infty}x^{\alpha}E||X|^{\beta}\cdot1_{\{|X|>x\}}|=0$

How to prove that the following estimators are biased and consistent?

CLT for decaying random variables

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