List questions from borel-cantelli-lemmas

Published on 18 Oct 2020 - 13:38

38

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Choosing positive reals $\alpha_i$ for $a_iX_i \sim N(0, a_i^2)$ such that $a_iX_i \stackrel{a.s.}{\to} 0$

Published on 22 Oct 2020 - 9:58

33

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Maximum length of consecutive 1's in a random 01 string

Published on 22 Oct 2020 - 16:32

127

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What's the probability for k consecutive 1s? I can use Borel-Cantelli

Published on 04 Nov 2020 - 10:44

61

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Borel-Cantelli Application Question

Published on 29 Nov 2020 - 1:14

99

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Sum of Indicators: $\sum_{n=1}^{\infty} \mathbb{1}\{X_1^2/\alpha^2 \geq n\} = \left(1 + \left\lfloor\frac{X_1^2}{\alpha^2}\right\rfloor\right)$

Published on 29 Nov 2020 - 5:24

261

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Understanding a definition of infinitely often

Published on 04 Dec 2020 - 21:10

159

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Theorem on lim sup of max of random variables.

Published on 05 Dec 2020 - 3:51

31

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Measure of a set with digits resemblance to $\pi$

Published on 11 Dec 2020 - 15:31

981

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Why almost sure convergence holds if $X_n = n$ w.p. $1/n$?

Published on 12 Dec 2020 - 14:14

81

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The divergence of a series implies the divergence of limit superior of absolute value of sums of random variables

Published on 21 Dec 2020 - 5:36

231

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Clarification on convergence almost surely

Published on 30 Dec 2020 - 3:10

66

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>Let $X_1,\ldots,X_n$ indepent variable RV $X_n\sim Bern(1/n)$ Does the $X_n\underset{a.s}{\to}0$

Published on 01 Jan 2021 - 11:28

27

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$X$ RV $X(S)=s$. Prove $X_n\underset{a.s}{\to}X$.

Published on 01 Jan 2021 - 11:56

135

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Convergence almost surely question

Published on 05 Jan 2021 - 0:49

List Question

Show that this sequence does not obey the SLLN

Choosing positive reals $\alpha_i$ for $a_iX_i \sim N(0, a_i^2)$ such that $a_iX_i \stackrel{a.s.}{\to} 0$

Maximum length of consecutive 1's in a random 01 string

What's the probability for k consecutive 1s? I can use Borel-Cantelli

Borel-Cantelli Application Question

Sum of Indicators: $\sum_{n=1}^{\infty} \mathbb{1}\{X_1^2/\alpha^2 \geq n\} = \left(1 + \left\lfloor\frac{X_1^2}{\alpha^2}\right\rfloor\right)$

Understanding a definition of infinitely often

Theorem on lim sup of max of random variables.

Measure of a set with digits resemblance to $\pi$

Why almost sure convergence holds if $X_n = n$ w.p. $1/n$?

The divergence of a series implies the divergence of limit superior of absolute value of sums of random variables

Clarification on convergence almost surely

>Let $X_1,\ldots,X_n$ indepent variable RV $X_n\sim Bern(1/n)$ Does the $X_n\underset{a.s}{\to}0$

$X$ RV $X(S)=s$. Prove $X_n\underset{a.s}{\to}X$.

Convergence almost surely question

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