Question

Conditions for monotonic convergence in the CLT?

score 155 · Answer 1 · 2026-04-01 03:47:53

155

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Conditions for monotonic convergence in the CLT?

Published on 01 Apr 2026 - 3:47

score 41 · Answer 2 · 2026-03-27 21:19:14

41

Views

Sample size vs. Number of samples (how many samples of size n will prove statistically significant results?)

Published on 27 Mar 2026 - 21:19

score 434 · Answer 3 · 2021-03-16 18:43:54

434

Views

Having $S_n$ being a sum of i.i.d. Bernoulli($p$) random variable, where does $S_n/\sqrt{n}$ converge to?

Published on 16 Mar 2021 - 18:43

score 405 · Answer 4 · 2021-03-17 02:42:58

405

Views

Getting a normal distribution when sampling a uniform disturbition

Published on 17 Mar 2021 - 2:42

score 46 · Answer 5 · 2021-03-18 18:18:03

46

Views

Test if coin is fair with significance/confidence of 95%

Published on 18 Mar 2021 - 18:18

score 26 · Answer 6 · 2021-03-19 07:22:02

26

Views

Use chebyshev's inequality to show that $P(S>22)\geq73/80$ and Use the central limit theorem to estimate $P(S>22)$

Published on 19 Mar 2021 - 7:22

score 217 · Answer 7 · 2026-03-26 06:19:12

217

Views

Original reference by Esseen for Berry-Esseen theorem

Published on 26 Mar 2026 - 6:19

score 69 · Answer 8 · 2021-03-19 22:37:55

69

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Convergence in distribution $\sqrt{n}X_n \xrightarrow{n \to +\infty} \mathcal{N}(0,1)$ implies $\sup_{n\in \Bbb N^*}E(|X_n|)<+\infty$

Published on 19 Mar 2021 - 22:37

score 34 · Answer 9 · 2021-04-06 06:48:34

34

Views

What am I doing wrong? Linear Combination of Normal Variables

Published on 06 Apr 2021 - 6:48

score 57 · Answer 10 · 2021-04-10 10:55:49

57

Views

Does a Binomial converge to Poisson or Normal?

Published on 10 Apr 2021 - 10:55

score 387 · Answer 11 · 2021-04-10 20:43:32

387

Views

How to prove that $\sqrt{n}(\ln S_n-\mu)$ converges in law to $\mathcal N(0,\sigma^2)$ where$S_n$is the logarithm of geometric mean of some iid $X_i$?

Published on 10 Apr 2021 - 20:43

score 655 · Answer 12 · 2026-02-23 19:44:57

655

Views

How does the Glivenko-Cantelli theorem improve the stochastic convergence of the empirical distribution $F_n(x)$?

Published on 23 Feb 2026 - 19:44

score 599 · Answer 13 · 2021-04-13 11:57:04

599

Views

Is sum of two asymptotically normal variables still asymptotically normal?

Published on 13 Apr 2021 - 11:57

score 79 · Answer 14 · 2021-04-14 03:28:09

79

Views

Simple(?) Central Limit Theorem Application- Magnitude of Gaussian Vector

Published on 14 Apr 2021 - 3:28

score 20 · Answer 15 · 2026-03-27 15:20:02

20

Views

Why does stating that the cdf $FZn(a) \to N(\mu,\sigma)$ leads to $P\{|Z_n - \mu| > \sigma\} = 1 - F_{Z_n}(\mu + \sigma) + F_{Z_n}((\mu + \sigma)^-)$?

Published on 27 Mar 2026 - 15:20

List Question

Conditions for monotonic convergence in the CLT?

Sample size vs. Number of samples (how many samples of size n will prove statistically significant results?)

Having $S_n$ being a sum of i.i.d. Bernoulli($p$) random variable, where does $S_n/\sqrt{n}$ converge to?

Getting a normal distribution when sampling a uniform disturbition

Test if coin is fair with significance/confidence of 95%

Use chebyshev's inequality to show that $P(S>22)\geq73/80$ and Use the central limit theorem to estimate $P(S>22)$

Original reference by Esseen for Berry-Esseen theorem

Convergence in distribution $\sqrt{n}X_n \xrightarrow{n \to +\infty} \mathcal{N}(0,1)$ implies $\sup_{n\in \Bbb N^*}E(|X_n|)<+\infty$

What am I doing wrong? Linear Combination of Normal Variables

Does a Binomial converge to Poisson or Normal?

How to prove that $\sqrt{n}(\ln S_n-\mu)$ converges in law to $\mathcal N(0,\sigma^2)$ where$S_n$is the logarithm of geometric mean of some iid $X_i$?

How does the Glivenko-Cantelli theorem improve the stochastic convergence of the empirical distribution $F_n(x)$?

Is sum of two asymptotically normal variables still asymptotically normal?

Simple(?) Central Limit Theorem Application- Magnitude of Gaussian Vector

Why does stating that the cdf $FZn(a) \to N(\mu,\sigma)$ leads to $P\{|Z_n - \mu| > \sigma\} = 1 - F_{Z_n}(\mu + \sigma) + F_{Z_n}((\mu + \sigma)^-)$?

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