List questions from probability-limit-theorems

39

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Double asymptotics: $E\|\mathbf{x}_n-\mathbf{z}\|_{\infty}^2 \to 0 \implies p^{-1}\mathbf{x}_n^\top\mathbf{x}_n\to 1$ as $(p,n) \to (\infty, \infty)$

Published on 27 Mar 2026 - 3:41

44

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Continuity set and his preimage in $f$

Published on 19 Feb 2023 - 7:40

148

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Two independent weak convergence sequences have dependent limit?

Published on 20 Feb 2023 - 14:08

263

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Two dimensional central limit theorem

Published on 20 Feb 2023 - 14:25

90

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Consistent or inconsistent estimator

Published on 22 Feb 2023 - 15:13

67

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Waiting times between record observations

Published on 25 Mar 2026 - 21:45

34

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Defining convergence of a sequence of random variables.

Published on 24 Feb 2026 - 23:15

24

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Prove $F(x-)\le\lim\inf F_n(x-)$ if $F_n\overset{d}{\rightarrow}F$

Published on 04 Mar 2023 - 14:59

66

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Probability for sometime vs after finite number?

Published on 04 Mar 2023 - 19:13

49

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Show that $F_n(x_n)-F(x_n)\rightarrow0$ as a corollary of Polya's theorem on $\mathbb{R}$

Published on 24 Feb 2026 - 23:12

103

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Proof of Helly Bray theorem: $X_n\overset{d}{\rightarrow}X\Leftrightarrow Eg(X_n)\rightarrow Eg(X)$ for bounded continuous $g$

Published on 05 Mar 2023 - 20:46

116

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Variance of sample fourth moment

Published on 08 Mar 2023 - 9:24

61

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Integrability of the suprenum of a sequence of random variables

Published on 17 Mar 2023 - 23:01

116

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Find limit of $(X_1...X_n)^{1/n}$ where $X_1,X_2,...$ are iid random variables uniformly distributed on interval $(1,2]$

Published on 17 Mar 2023 - 23:22

41

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Test scores have mean $7.4$ and variance $1.2$. The teacher is in charge of two courses of $40$ students each.

Published on 17 Mar 2023 - 23:45

List Question

Double asymptotics: $E\|\mathbf{x}_n-\mathbf{z}\|_{\infty}^2 \to 0 \implies p^{-1}\mathbf{x}_n^\top\mathbf{x}_n\to 1$ as $(p,n) \to (\infty, \infty)$

Continuity set and his preimage in $f$

Two independent weak convergence sequences have dependent limit?

Two dimensional central limit theorem

Consistent or inconsistent estimator

Waiting times between record observations

Defining convergence of a sequence of random variables.

Prove $F(x-)\le\lim\inf F_n(x-)$ if $F_n\overset{d}{\rightarrow}F$

Probability for sometime vs after finite number?

Show that $F_n(x_n)-F(x_n)\rightarrow0$ as a corollary of Polya's theorem on $\mathbb{R}$

Proof of Helly Bray theorem: $X_n\overset{d}{\rightarrow}X\Leftrightarrow Eg(X_n)\rightarrow Eg(X)$ for bounded continuous $g$

Variance of sample fourth moment

Integrability of the suprenum of a sequence of random variables

Find limit of $(X_1...X_n)^{1/n}$ where $X_1,X_2,...$ are iid random variables uniformly distributed on interval $(1,2]$

Test scores have mean $7.4$ and variance $1.2$. The teacher is in charge of two courses of $40$ students each.

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