List questions from probability-limit-theorems

Published on 24 Mar 2026 - 20:27

62

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Estimators and Confidence intervals

Published on 25 Mar 2026 - 1:58

65

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$\lim_{n \to \infty} E[e^{-X\frac{t}{n}}]^n \approx \lim_{n \to \infty} E(1-\frac{E[X] t}{n})^n = e^{-E[X]t}$

Published on 25 Mar 2026 - 4:15

82

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Asymptotic independence on the tail field is equivalent to a probability measure's being trivial

Published on 24 Mar 2026 - 19:03

164

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Lindeberg CLT condition on Discrete Uniform independent sequence of random variables

Published on 25 Mar 2026 - 9:04

72

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Convergence of the sum of iid scaled by $n^\alpha$

Published on 25 Mar 2026 - 10:53

494

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Asymptotics of expected value of maximum of normal variables

Published on 25 Mar 2026 - 4:34

49

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Central Limit Theorem- Lapunow, Linderberg

Published on 24 Mar 2026 - 0:20

394

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Tail weight of product distributions

Published on 21 Feb 2019 - 1:02

123

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Why this sequence converges to $0$ and not to $1$ in probability?

Published on 24 Mar 2026 - 17:36

601

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Polya's theorem implies Glivenko-Cantelli for continuous distributions

Published on 25 Mar 2026 - 9:12

541

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Application of Kolmogorov 0-1 Law for $S_x := \{\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{i=1}^{n}1_{A_{i}}\leq x\}$

Published on 24 Mar 2026 - 3:02

158

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Tilted sum of independent random variables

Published on 24 Mar 2026 - 21:52

2.1k

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Tail event example

Published on 24 Mar 2026 - 17:32

101

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Why this sequence of R.V converge in distribution, but doesnt in probability

Published on 23 Mar 2026 - 20:33

List Question

independence implies integrability?!

Estimators and Confidence intervals

$\lim_{n \to \infty} E[e^{-X\frac{t}{n}}]^n \approx \lim_{n \to \infty} E(1-\frac{E[X] t}{n})^n = e^{-E[X]t}$

Asymptotic independence on the tail field is equivalent to a probability measure's being trivial

Lindeberg CLT condition on Discrete Uniform independent sequence of random variables

Convergence of the sum of iid scaled by $n^\alpha$

Asymptotics of expected value of maximum of normal variables

Central Limit Theorem- Lapunow, Linderberg

Tail weight of product distributions

Why this sequence converges to $0$ and not to $1$ in probability?

Polya's theorem implies Glivenko-Cantelli for continuous distributions

Application of Kolmogorov 0-1 Law for $S_x := \{\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{i=1}^{n}1_{A_{i}}\leq x\}$

Tilted sum of independent random variables

Tail event example

Why this sequence of R.V converge in distribution, but doesnt in probability

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