Question

$\{X_n\}$ i.i.d. with mean zero and finite variance. Prove that $\lim\limits_n E[|S_n|/\sqrt n]=2\lim\limits_n E[S_n^+/\sqrt n]=\sqrt{2/\pi}\sigma$

score 174 · Answer 1 · 2022-12-12 13:08:10

174

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$\{X_n\}$ i.i.d. with mean zero and finite variance. Prove that $\lim\limits_n E[|S_n|/\sqrt n]=2\lim\limits_n E[S_n^+/\sqrt n]=\sqrt{2/\pi}\sigma$

Published on 12 Dec 2022 - 13:08

score 81 · Answer 2 · 2026-03-28 09:57:36

81

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Let X(X bar) denote the mean of a random sample of size 36 for Chi-squared distribution with 2 degrees of freedom.Find P(1.75 <X<2.5)

Published on 28 Mar 2026 - 9:57

score 35 · Answer 3 · 2022-12-14 11:17:38

35

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Prove $\frac{\sum_{j=1}^nX_j}{\sqrt{\sum_{j=1}^nX_j^2}}$ converges to $\mathcal{N}(0,1)$ in distribution

Published on 14 Dec 2022 - 11:17

score 26 · Answer 4 · 2026-04-02 10:07:40

26

Views

Is it the sampling process, not the population distribution, that makes the CLT central limit theorem work?

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score 72 · Answer 5 · 2026-03-28 00:28:47

72

Views

Threefold Convolution of a Schwartz function produces the same gaussian

Published on 28 Mar 2026 - 0:28

score 54 · Answer 6 · 2022-12-18 08:40:48

54

Views

$\lim_{N\to\infty} \frac{1}{N} \sum_{i=1}^N f(X_i)=\mathbb{E}[f(x)]$

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score 491 · Answer 7 · 2026-03-31 22:49:23

491

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Understanding Central Limit Theorem vs. Law of Large Numbers

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score 50 · Answer 8 · 2026-03-31 22:44:39

50

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score 176 · Answer 9 · 2022-12-25 13:01:18

176

Views

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score 112 · Answer 10 · 2022-12-29 13:56:46

112

Views

$\{X_i\}$ i.d normally distributed r.v.$E(X_n)=0,Var(X_n)=1+1/n$,judge whether $\{X_n\}$ satisfies CLT?

Published on 29 Dec 2022 - 13:56

score 108 · Answer 11 · 2023-01-03 19:34:40

108

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Published on 03 Jan 2023 - 19:34

score 190 · Answer 12 · 2023-01-12 07:58:43

190

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score 97 · Answer 13 · 2023-01-21 14:26:29

97

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score 77 · Answer 14 · 2023-01-23 13:20:40

77

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Published on 23 Jan 2023 - 13:20

score 189 · Answer 15 · 2023-01-26 04:11:06

189

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Probability that the Median is Below a Certain Number?

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List Question

$\{X_n\}$ i.i.d. with mean zero and finite variance. Prove that $\lim\limits_n E[|S_n|/\sqrt n]=2\lim\limits_n E[S_n^+/\sqrt n]=\sqrt{2/\pi}\sigma$

Let X(X bar) denote the mean of a random sample of size 36 for Chi-squared distribution with 2 degrees of freedom.Find P(1.75 <X<2.5)

Prove $\frac{\sum_{j=1}^nX_j}{\sqrt{\sum_{j=1}^nX_j^2}}$ converges to $\mathcal{N}(0,1)$ in distribution

Is it the sampling process, not the population distribution, that makes the CLT central limit theorem work?

Threefold Convolution of a Schwartz function produces the same gaussian

$\lim_{N\to\infty} \frac{1}{N} \sum_{i=1}^N f(X_i)=\mathbb{E}[f(x)]$

Understanding Central Limit Theorem vs. Law of Large Numbers

Upper bound in context of local limit theorem

Fastest way to converge to mean

$\{X_i\}$ i.d normally distributed r.v.$E(X_n)=0,Var(X_n)=1+1/n$,judge whether $\{X_n\}$ satisfies CLT?

How to get the distribution of a random variable from the distribution of their summation?

Different methods for sample size estimates of a binomial

Probability for total score after rolling a die $n$ times

What is the probability that a randomly chosen fetal heartrate differs from the mean by more than 25 bpm?

Probability that the Median is Below a Certain Number?

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