List questions from probability-limit-theorems

Published on 23 Feb 2026 - 20:42

133

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$X \geq 0$, $E[X] =\infty$. What's a lower bound for speed at which sample mean $\overline X_n$ diverges toward $\infty$?

Published on 12 Jan 2022 - 22:55

130

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Probability that in an endless series of independent Bernoulli trials, the pattern of $101$ will appear infinite times?

Published on 16 Jan 2022 - 15:06

220

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Stuck on proving a variation of the Central Limit Theorem.

Published on 17 Jan 2022 - 22:12

63

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Almost-sure convergence of a series of log-normal random variables

Published on 27 Mar 2026 - 7:49

199

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Estimating operator norm with random variables

Published on 28 Mar 2026 - 9:24

222

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How to show that $\frac{1}{X_n}\to 1/c \, \mbox{ in probability} $?

Published on 19 Jan 2022 - 1:01

62

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Show $\lim_{n \to \infty} \mathbb{E} [ f(S_n) \mid S_n \geq t] \mathbb{P}(S_n \geq t) = 0$

Published on 26 Mar 2026 - 3:01

186

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Exercise about almost sure convergence

Published on 20 Jan 2022 - 8:49

285

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Showing that a series of random variables converges almost surely.

Published on 20 Jan 2022 - 16:59

105

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Triangular array of non-independent elements each row

Published on 20 Jan 2022 - 22:04

39

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Confusion when using continuity of the $\Phi$ function for convergence in probability

Published on 21 Jan 2022 - 8:41

121

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Non-standardised central limit theorem

Published on 28 Mar 2026 - 4:52

113

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Given a triangular array of r.v.s so that each column converges in probability to $0$. Can we say that the row-wise averages converge to $0$?

Published on 22 Jan 2022 - 16:53

74

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How to prove the limit of the empirical distribution function?

Published on 24 Jan 2022 - 1:38

List Question

How to prove CLT for predictable quadratic variation $\langle X_n \rangle$ for a martingale $X_n$

$X \geq 0$, $E[X] =\infty$. What's a lower bound for speed at which sample mean $\overline X_n$ diverges toward $\infty$?

Probability that in an endless series of independent Bernoulli trials, the pattern of $101$ will appear infinite times?

Stuck on proving a variation of the Central Limit Theorem.

Almost-sure convergence of a series of log-normal random variables

Estimating operator norm with random variables

How to show that $\frac{1}{X_n}\to 1/c \, \mbox{ in probability} $?

Show $\lim_{n \to \infty} \mathbb{E} [ f(S_n) \mid S_n \geq t] \mathbb{P}(S_n \geq t) = 0$

Exercise about almost sure convergence

Showing that a series of random variables converges almost surely.

Triangular array of non-independent elements each row

Confusion when using continuity of the $\Phi$ function for convergence in probability

Non-standardised central limit theorem

Given a triangular array of r.v.s so that each column converges in probability to $0$. Can we say that the row-wise averages converge to $0$?

How to prove the limit of the empirical distribution function?

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