Question

Stuck on proving a variation of the Central Limit Theorem.

score 221 · Answer 1 · 2026-04-01 17:27:57

221

Views

Stuck on proving a variation of the Central Limit Theorem.

Published on 01 Apr 2026 - 17:27

score 59 · Answer 2 · 2022-01-18 21:17:02

59

Views

Show that $P\left ( \left | \sum_{i=1}^{n}X_i \right |\leq 2\sqrt{n} \right )\to 1-2\Phi(-2)$ - solution explanation

Published on 18 Jan 2022 - 21:17

score 121 · Answer 3 · 2026-03-28 04:52:11

121

Views

Non-standardised central limit theorem

Published on 28 Mar 2026 - 4:52

score 28 · Answer 4 · 2022-01-28 19:51:51

28

Views

$X \overset{d}{\longrightarrow} N(0,\sigma ^2) \implies \frac{X}{\sqrt{S_n ^2}} \overset{d}{\longrightarrow} N(0,1)$?

Published on 28 Jan 2022 - 19:51

score 547 · Answer 5 · 2026-04-02 07:53:53

547

Views

Convergence in distribution of the two-sample $t$-test statistic

Published on 02 Apr 2026 - 7:53

score 64 · Answer 6 · 2022-02-03 08:06:32

64

Views

Central Limit Theorem and Convergence

Published on 03 Feb 2022 - 8:06

score 114 · Answer 7 · 2022-02-04 19:59:50

114

Views

Find the limiting distribution of $\frac{\sum_{i=1}^{n}(Y_i^2-\sigma Z_i^2)}{\sum_{i=1}^{n}Z_i^2}$, where $Z_i\sim N(0,1)$ and $Y_i\sim N(0,\sigma^2)$

Published on 04 Feb 2022 - 19:59

score 405 · Answer 8 · 2022-02-06 15:42:28

405

Views

Approximate the distribution of a random variable if n is large enough?

Published on 06 Feb 2022 - 15:42

score 135 · Answer 9 · 2026-04-01 18:47:29

135

Views

Assume $X_i$ are i.i.d, from Poisson$(\lambda)$ distribution for some $\lambda >0$, Show $\sqrt{n}(1/\bar{X}-1/\lambda)\to_D N(0,\sigma_{\lambda}^2)$

Published on 01 Apr 2026 - 18:47

score 252 · Answer 10 · 2026-04-01 23:29:56

252

Views

Are sample (mean) distributions continuous and have exact PDFs?

Published on 01 Apr 2026 - 23:29

score 39 · Answer 11 · 2026-03-26 02:47:35

39

Views

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

score 98 · Answer 12 · 2026-04-01 20:24:00

98

Views

Ensure Convergence to non degenerate limit

Published on 01 Apr 2026 - 20:24

score 838 · Answer 13 · 2026-04-01 20:25:30

838

Views

Asymptotic normality of estimator of uniform's distribution parameter

Published on 01 Apr 2026 - 20:25

score 155 · Answer 14 · 2026-03-28 04:35:50

155

Views

What went wrong in my application of the Martingale Central Limit Theorem to a degenerate U-statistic?

Published on 28 Mar 2026 - 4:35

score 30 · Answer 15 · 2022-02-23 11:44:53

30

Views

Inverse of a positive symmetric matrix with large entries

Published on 23 Feb 2022 - 11:44

List Question

Stuck on proving a variation of the Central Limit Theorem.

Show that $P\left ( \left | \sum_{i=1}^{n}X_i \right |\leq 2\sqrt{n} \right )\to 1-2\Phi(-2)$ - solution explanation

Non-standardised central limit theorem

$X \overset{d}{\longrightarrow} N(0,\sigma ^2) \implies \frac{X}{\sqrt{S_n ^2}} \overset{d}{\longrightarrow} N(0,1)$?

Convergence in distribution of the two-sample $t$-test statistic

Central Limit Theorem and Convergence

Find the limiting distribution of $\frac{\sum_{i=1}^{n}(Y_i^2-\sigma Z_i^2)}{\sum_{i=1}^{n}Z_i^2}$, where $Z_i\sim N(0,1)$ and $Y_i\sim N(0,\sigma^2)$

Approximate the distribution of a random variable if n is large enough?

Assume $X_i$ are i.i.d, from Poisson$(\lambda)$ distribution for some $\lambda >0$, Show $\sqrt{n}(1/\bar{X}-1/\lambda)\to_D N(0,\sigma_{\lambda}^2)$

Are sample (mean) distributions continuous and have exact PDFs?

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

Asymptotic normality of estimator of uniform's distribution parameter

What went wrong in my application of the Martingale Central Limit Theorem to a degenerate U-statistic?

Inverse of a positive symmetric matrix with large entries

Trending Questions

Popular # Hahtags

Popular Questions