List questions from probability-limit-theorems

Published on 29 Mar 2026 - 13:21

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classification of rational and irrational via one-nearest neighbor

Published on 26 Jan 2022 - 16:44

212

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Applications of Fatou's lemma and Borel-Cantelli lemma

Published on 27 Mar 2026 - 13:47

126

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Checking uniform integrability of random series

Published on 27 Mar 2026 - 12:15

19

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Constructing a decreasing sequence that converges to $0$ in probability given convergence in probability to $0$

Published on 30 Jan 2022 - 0:09

62

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Bounded in probability of the running maximum of a stopped process implies almost sure boundedness on the interval $[0,\lim \tau_r)$?

Published on 30 Jan 2022 - 1:03

168

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$\lim\sup$ and $\lim\inf$ of a sequence of independent random variables with two states

Published on 31 Jan 2022 - 12:44

45

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Limit Theory for Strongly Dependent Random Variables

Published on 31 Jan 2022 - 23:08

44

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Show that $\sum_{n=0}^{\infty}E[X \mathbf{1}_{A_n}] = E[X\mathbf{1}_A]$

Published on 31 Jan 2022 - 23:42

86

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Lower bound on the probability of a sum of iid random variables larger than a threshold

Published on 28 Mar 2026 - 14:25

129

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Resnick -Probability Path - Exercise 7.40

Published on 05 Feb 2022 - 2:19

87

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$\max\{ aX_n, b Y_n\} \to \max\{aX,bY\}$

Published on 06 Feb 2022 - 19:12

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Assume $X_i$ are i.i.d, from Poisson$(\lambda)$ distribution for some $\lambda >0$, Show $\sqrt{n}(1/\bar{X}-1/\lambda)\to_D N(0,\sigma_{\lambda}^2)$

Published on 08 Feb 2022 - 12:22

208

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Almost surely converges for product of Uniform[0,1.1] using defention

Published on 27 Mar 2026 - 13:47

30

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Convergence of random series based on iid standard gaussian variables

Published on 09 Feb 2022 - 17:42

List Question

almost sure convergence via subsequence arguments

classification of rational and irrational via one-nearest neighbor

Applications of Fatou's lemma and Borel-Cantelli lemma

Checking uniform integrability of random series

Constructing a decreasing sequence that converges to $0$ in probability given convergence in probability to $0$

Bounded in probability of the running maximum of a stopped process implies almost sure boundedness on the interval $[0,\lim \tau_r)$?

$\lim\sup$ and $\lim\inf$ of a sequence of independent random variables with two states

Limit Theory for Strongly Dependent Random Variables

Show that $\sum_{n=0}^{\infty}E[X \mathbf{1}_{A_n}] = E[X\mathbf{1}_A]$

Lower bound on the probability of a sum of iid random variables larger than a threshold

Resnick -Probability Path - Exercise 7.40

$\max\{ aX_n, b Y_n\} \to \max\{aX,bY\}$

Assume $X_i$ are i.i.d, from Poisson$(\lambda)$ distribution for some $\lambda >0$, Show $\sqrt{n}(1/\bar{X}-1/\lambda)\to_D N(0,\sigma_{\lambda}^2)$

Almost surely converges for product of Uniform[0,1.1] using defention

Convergence of random series based on iid standard gaussian variables

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