List questions from probability-limit-theorems

75

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Show that if $\mathbb{E}X_n = 0$ and $\sup\limits_{n \in \mathbb{N}} \mathbb{E}|X_n|^4 \leq C$ then $\frac{1}{n} (X_1+\dots+X_n) \to 0$ almost surely

Published on 04 Feb 2021 - 20:37

243

Views

Why would a 1-in-a-billion years event happening be suprising if it happens once?

Published on 05 Feb 2021 - 2:19

114

Views

Convergence of $\mathbb{E}[f]$ over Poisson/Binomial $\mathbb{E}_{X\sim\text{Bin}(n,\lambda/n)}[f]\rightarrow\mathbb{E}_{X\sim\text{Poi}(\lambda)}[f]$

Published on 06 Feb 2021 - 20:22

176

Views

Why do my Stack Exchange reps follow a power law?

Published on 08 Feb 2021 - 7:32

755

Views

Prove that MGF defined on an open set is infinitely differentiable

Published on 31 Mar 2026 - 10:07

80

Views

Convergence of a weighted discrete measure

Published on 10 Feb 2021 - 0:15

171

Views

Law of large number integral asymptotic results

Published on 30 Mar 2026 - 23:12

84

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a.s convergence of a series

Published on 13 Feb 2021 - 0:51

131

Views

Normalized sum converges in distribution to $N(0,1)$

Published on 16 Feb 2021 - 17:09

80

Views

poisson process limit, SLLN

Published on 31 Mar 2026 - 19:48

97

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Proof of Weak Law of Large Numbers with non-zero covariance

Published on 30 Mar 2026 - 23:13

55

Views

Is there any method to solve this probability and find an closed form expression?

Published on 31 Mar 2026 - 19:13

180

Views

Derivative of conditional expectation of integral of stochastic process

Published on 30 Mar 2026 - 16:54

1k

Views

If $X_n \to X $ in probability then $f(X_n) \to f(X)$ in probability for a Borel function $f$

Published on 25 Feb 2021 - 20:11

175

Views

Does the law of large numbers hold for covering numbers?

Published on 23 Feb 2026 - 8:03

List Question

Show that if $\mathbb{E}X_n = 0$ and $\sup\limits_{n \in \mathbb{N}} \mathbb{E}|X_n|^4 \leq C$ then $\frac{1}{n} (X_1+\dots+X_n) \to 0$ almost surely

Why would a 1-in-a-billion years event happening be suprising if it happens once?

Convergence of $\mathbb{E}[f]$ over Poisson/Binomial $\mathbb{E}_{X\sim\text{Bin}(n,\lambda/n)}[f]\rightarrow\mathbb{E}_{X\sim\text{Poi}(\lambda)}[f]$

Why do my Stack Exchange reps follow a power law?

Prove that MGF defined on an open set is infinitely differentiable

Convergence of a weighted discrete measure

Law of large number integral asymptotic results

a.s convergence of a series

Normalized sum converges in distribution to $N(0,1)$

poisson process limit, SLLN

Proof of Weak Law of Large Numbers with non-zero covariance

Is there any method to solve this probability and find an closed form expression?

Derivative of conditional expectation of integral of stochastic process

If $X_n \to X $ in probability then $f(X_n) \to f(X)$ in probability for a Borel function $f$

Does the law of large numbers hold for covering numbers?

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