Question

Borell-Cantelli lemma

score 64 · Answer 1 · 2020-04-22 16:05:43

64

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Borell-Cantelli lemma

Published on 22 Apr 2020 - 16:05

score 330 · Answer 2 · 2020-04-27 07:45:51

330

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Convergence of Maximum of $n$ i.i.d. random variables in probability and almost surely

Published on 27 Apr 2020 - 7:45

score 294 · Answer 3 · 2020-04-29 11:34:56

For independent random variables $X_n$, how to prove $X_n / n^p \rightarrow 0$ a.s. iff $E\left(\left|X_{n}\right|^{1 / p}\right)<\infty$ for $p>0$

score 319 · Answer 4 · 2020-05-02 22:18:19

319

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Infinite coin tosses- same number of heads and tails will occur infinitely many times

Published on 02 May 2020 - 22:18

score 399 · Answer 5 · 2020-05-06 10:03:47

399

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Borel-Cantelli argument for maximum of random variables

Published on 06 May 2020 - 10:03

score 54 · Answer 6 · 2020-05-06 11:16:46

54

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How is the Borel-Cantelli lemma applied here?

Published on 06 May 2020 - 11:16

score 142 · Answer 7 · 2020-05-08 19:59:36

142

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Question on a application of Borel-Cantelli Lemma and answer veryfication

Published on 08 May 2020 - 19:59

score 661 · Answer 8 · 2020-05-14 02:20:22

661

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Converse of Borel-Cantelli

Published on 14 May 2020 - 2:20

score 176 · Answer 9 · 2020-05-18 14:11:32

176

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Prove SLLN doesn't hold for a given series of random variables

Published on 18 May 2020 - 14:11

score 42 · Answer 10 · 2020-05-19 18:14:24

42

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$E[|X|^r]=+\infty$ $\implies$ $P(\left\{\limsup_nY_n=+\infty \right\}\cup\left\{\liminf_nY_n=-\infty \right\})=1?!$

Published on 19 May 2020 - 18:14

score 48 · Answer 11 · 2020-05-26 18:55:40

48

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I don't get it why the Second Borel Cantelli Lemma here will get me to this conclusion, I don't see the link

Published on 26 May 2020 - 18:55

score 483 · Answer 12 · 2020-06-01 00:23:45

483

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$X_1,X_2, \ldots$ be i.i.d. Show that $\mathbb{E}|X_1| < \infty $ iff $ \frac{X_n}{n} \to 0$ a.s

Published on 01 Jun 2020 - 0:23

score 788 · Answer 13 · 2020-06-02 00:18:41

788

Views

Sum of independent random variables is a martingale which converges almost surely

Published on 02 Jun 2020 - 0:18

score 55 · Answer 14 · 2026-03-25 08:12:56

55

Views

Why sets of nonzero measure contain almost all the point from Borel-cantelli Leems?

Published on 25 Mar 2026 - 8:12

score 91 · Answer 15 · 2026-03-25 17:26:52

91

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Show that $\log{M_n}/\log{n}\to1$ a.s. where $M_n = \max\{X_k \mid 1 \leq k \leq n\}$ and the $X_n$ are iid with $\mathbb{P}(X_n \geq i) = 1/i$.

Published on 25 Mar 2026 - 17:26

List Question

Borell-Cantelli lemma

Convergence of Maximum of $n$ i.i.d. random variables in probability and almost surely

For independent random variables $X_n$, how to prove $X_n / n^p \rightarrow 0$ a.s. iff $E\left(\left|X_{n}\right|^{1 / p}\right)<\infty$ for $p>0$

Infinite coin tosses- same number of heads and tails will occur infinitely many times

Borel-Cantelli argument for maximum of random variables

How is the Borel-Cantelli lemma applied here?

Question on a application of Borel-Cantelli Lemma and answer veryfication

Converse of Borel-Cantelli

Prove SLLN doesn't hold for a given series of random variables

$E[|X|^r]=+\infty$ $\implies$ $P(\left\{\limsup_nY_n=+\infty \right\}\cup\left\{\liminf_nY_n=-\infty \right\})=1?!$

I don't get it why the Second Borel Cantelli Lemma here will get me to this conclusion, I don't see the link

$X_1,X_2, \ldots$ be i.i.d. Show that $\mathbb{E}|X_1| < \infty $ iff $ \frac{X_n}{n} \to 0$ a.s

Sum of independent random variables is a martingale which converges almost surely

Why sets of nonzero measure contain almost all the point from Borel-cantelli Leems?

Show that $\log{M_n}/\log{n}\to1$ a.s. where $M_n = \max\{X_k \mid 1 \leq k \leq n\}$ and the $X_n$ are iid with $\mathbb{P}(X_n \geq i) = 1/i$.

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