List questions from central-limit-theorem

Published on 26 Feb 2023 - 5:53

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Can the sample mean converge faster than $1/\sqrt{n}$?

Published on 03 Mar 2023 - 13:57

42

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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 27 Mar 2026 - 22:53

232

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Convergence of the central limit theorem: pointwise vs uniform convergence

Published on 23 Mar 2023 - 11:10

206

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CLT as a special case of the Banach fixed-point theorem?

Published on 27 Feb 2026 - 16:34

60

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$MA(q)$ : Show $\sqrt{n}\hat{\rho}(q + l)\underrightarrow{d} N(0, 1 + 2\sum _{j=1}^q\rho ^2\left(j\right)), l\ge 1 $

Published on 27 Mar 2026 - 6:09

120

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Limit of the sum of independent random variables $(X_i)_{n \geq 1}$ but with $\sum_i \operatorname{Var}(X_i) < \infty$.

Published on 28 Mar 2026 - 2:06

36

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Central Limit Theorem - question terminology?

Published on 30 Mar 2023 - 20:00

82

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Given random variables $S_n \sim \mathrm{Pois}(n)$, can we think $S_n=X_1+X_2+...+X_n$ where $X_i \sim \mathrm{Pois}(1)$?

Published on 31 Mar 2023 - 21:04

756

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Central Limit Theorem without IID?

Published on 01 Apr 2023 - 16:56

226

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Binomial convergence to Normal

Published on 28 Mar 2026 - 2:09

40

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Limit of Polynomial Resembling Gaussian

Published on 28 Mar 2026 - 2:04

140

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Applying Central Limit Theorem

Published on 28 Mar 2026 - 2:09

414

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Assumption of Normality in Central Limit Theorem

Published on 29 Mar 2026 - 10:48

35

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Can you have a concentration result for $1/\sqrt{n}$ deviation?

Published on 27 Mar 2026 - 11:24

List Question

Stochastic continuity and Lindeberg's condition.

Can the sample mean converge faster than $1/\sqrt{n}$?

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

Convergence of the central limit theorem: pointwise vs uniform convergence

CLT as a special case of the Banach fixed-point theorem?

$MA(q)$ : Show $\sqrt{n}\hat{\rho}(q + l)\underrightarrow{d} N(0, 1 + 2\sum _{j=1}^q\rho ^2\left(j\right)), l\ge 1 $

Limit of the sum of independent random variables $(X_i)_{n \geq 1}$ but with $\sum_i \operatorname{Var}(X_i) < \infty$.

Central Limit Theorem - question terminology?

Given random variables $S_n \sim \mathrm{Pois}(n)$, can we think $S_n=X_1+X_2+...+X_n$ where $X_i \sim \mathrm{Pois}(1)$?

Central Limit Theorem without IID?

Binomial convergence to Normal

Limit of Polynomial Resembling Gaussian

Applying Central Limit Theorem

Assumption of Normality in Central Limit Theorem

Can you have a concentration result for $1/\sqrt{n}$ deviation?

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