List questions from probability-limit-theorems

Published on 13 Feb 2022 - 14:11

187

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$X_n \ \xrightarrow{p}\ 0$. However, the expected value of $X_n$ does not converge to $0$

Published on 14 Feb 2022 - 7:24

449

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Proof of Attenuation Bias

Published on 14 Feb 2022 - 14:57

39

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Let $Y=g(X)$ with $X\sim F_X$ and $Y^\ast=g(\mu_X)+g^\prime(\mu_X)(X-\mu_X)$. Under what conditions does $Y\overset{d}{\to}Y^\ast$?

Published on 26 Mar 2026 - 2:47

97

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Ensure Convergence to non degenerate limit

Published on 15 Feb 2022 - 5:26

24

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Generalizing stable and max-stable random variables using limit theorems for functions of random variables beyond Sum and Max?

Published on 17 Feb 2022 - 20:52

132

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Almost sure convergence of the sequence of partial averages of a random variable $T_n = X*\mathbb{1}_{X_n \geq X}$

Published on 19 Feb 2022 - 15:24

26

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Right continuity of the cumulative distribution function and an almost sure constant $X$

Published on 28 Mar 2026 - 6:40

837

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Asymptotic normality of estimator of uniform's distribution parameter

Published on 20 Feb 2022 - 19:12

275

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Sample Pearson correlation coefficient

Published on 20 Feb 2022 - 22:08

37

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Property of sums of independent and identically distributed random variables

Published on 25 Feb 2022 - 7:51

76

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A question regarding the central limit theorem

Published on 26 Feb 2022 - 19:41

54

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Convergence in probability and convergence in distribution in the context of OLS

Published on 02 Mar 2022 - 15:38

61

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For i.i.d sequence of random vectors $(X_i,Y_i), i=1,...,n)$ show that $\sqrt{n}(\bar{XY}- \bar X\bar Y -E(XY)+E(X)E(Y)) \to_d N(0,\alpha^2)$

Published on 02 Mar 2022 - 21:29

55

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Why is $ \mathbb{E} \limsup\limits_{n\rightarrow\infty}X_n = \mathbb{E} \lim\limits_{n\rightarrow \infty} X_n$

Published on 04 Mar 2022 - 2:30

List Question

Central limit theorem and convergence of tails

$X_n \ \xrightarrow{p}\ 0$. However, the expected value of $X_n$ does not converge to $0$

Proof of Attenuation Bias

Let $Y=g(X)$ with $X\sim F_X$ and $Y^\ast=g(\mu_X)+g^\prime(\mu_X)(X-\mu_X)$. Under what conditions does $Y\overset{d}{\to}Y^\ast$?

Ensure Convergence to non degenerate limit

Generalizing stable and max-stable random variables using limit theorems for functions of random variables beyond Sum and Max?

Almost sure convergence of the sequence of partial averages of a random variable $T_n = X*\mathbb{1}_{X_n \geq X}$

Right continuity of the cumulative distribution function and an almost sure constant $X$

Asymptotic normality of estimator of uniform's distribution parameter

Sample Pearson correlation coefficient

Property of sums of independent and identically distributed random variables

A question regarding the central limit theorem

Convergence in probability and convergence in distribution in the context of OLS

For i.i.d sequence of random vectors $(X_i,Y_i), i=1,...,n)$ show that $\sqrt{n}(\bar{XY}- \bar X\bar Y -E(XY)+E(X)E(Y)) \to_d N(0,\alpha^2)$

Why is $ \mathbb{E} \limsup\limits_{n\rightarrow\infty}X_n = \mathbb{E} \lim\limits_{n\rightarrow \infty} X_n$

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