List questions from law-of-large-numbers

Published on 15 Apr 2026 - 5:41

384

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probability random sample mean and variance

Published on 13 Apr 2026 - 11:39

251

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Finding the distribution when $n$ goes to infinity

Published on 10 Apr 2026 - 0:52

202

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Finding the distribution of a sequence of random variables

Published on 09 Apr 2026 - 1:16

223

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Law of large numbers question

Published on 10 Apr 2026 - 3:16

124

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Strong Law of Large Numbers with randomly many summands

Published on 12 Apr 2026 - 3:45

165

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An upper bound for $\sum_{n=1}^{\infty} n^{r-2} P\{|\sum_{k=1}^{n} \sum_{i=-\infty}^{\infty} a_{i} X_{i+k}|>\varepsilon n\}$

Published on 15 Apr 2026 - 6:10

71

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Does the convergence of $X_n$ in probability implies the convergence of $(X_1 + \cdots + X_n) / n$?

Published on 14 Apr 2026 - 20:42

198

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Prove that if the series is convergent then the law of large numbers hold.

Published on 14 Apr 2026 - 12:02

212

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Show integrability given tail probability goes to zero

Published on 15 Apr 2026 - 0:00

36

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Nontrivial lower-bound for $\lim\sup_n P(|X_n| / (Y_n^2+Z_n^2) \le t) $ if $X_n,Y_n,Z_n \to N(0,1)$ in distribution

Published on 17 Apr 2026 - 15:52

215

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Central Limit Theorem and Strong Law of Large Numbers. Proof that converges in distribution to $N(0, e^2)$

Published on 16 Apr 2026 - 17:05

69

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Difference in probability between the number of heads and the proportion of heads, in independent tosses of a fair coin.

Published on 16 Apr 2026 - 10:15

58

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Expectation of Reciprocal of Average of Variables.

Published on 12 Apr 2026 - 16:02

195

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An intuitive explanation for two applications of the Borel-Cantelli Lemma

Published on 12 Apr 2026 - 13:19

List Question

using Chebyshev's inequality

probability random sample mean and variance

Finding the distribution when $n$ goes to infinity

Finding the distribution of a sequence of random variables

Law of large numbers question

Strong Law of Large Numbers with randomly many summands

An upper bound for $\sum_{n=1}^{\infty} n^{r-2} P\{|\sum_{k=1}^{n} \sum_{i=-\infty}^{\infty} a_{i} X_{i+k}|>\varepsilon n\}$

Does the convergence of $X_n$ in probability implies the convergence of $(X_1 + \cdots + X_n) / n$?

Prove that if the series is convergent then the law of large numbers hold.

Show integrability given tail probability goes to zero

Nontrivial lower-bound for $\lim\sup_n P(|X_n| / (Y_n^2+Z_n^2) \le t) $ if $X_n,Y_n,Z_n \to N(0,1)$ in distribution

Central Limit Theorem and Strong Law of Large Numbers. Proof that converges in distribution to $N(0, e^2)$

Difference in probability between the number of heads and the proportion of heads, in independent tosses of a fair coin.

Expectation of Reciprocal of Average of Variables.

An intuitive explanation for two applications of the Borel-Cantelli Lemma

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