List questions from central-limit-theorem

Published on 27 Mar 2026 - 10:07

64

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"Show experimentally" that for large $N$, $X$ appears to be normally distributed.

Published on 14 Jun 2014 - 12:47

71

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Use central limit theorem to find variance

Published on 19 Jun 2014 - 13:04

262

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if $X_i$ are iid standard normal distributed, what is the limiting distribution of $\sum X^4 / (\sum X^2)^2$?

Published on 21 Jun 2014 - 21:00

956

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Central Limit Theorem not valid?

Published on 29 Jun 2014 - 17:14

93

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Show $\lim_{n\to\infty}\sqrt{n}\bigg(\frac{\sum_{j=1}^{n}X_j}{\sum_{j=1}^{n}X_j^2}\bigg)=Z$

Published on 03 Jul 2014 - 16:18

1.3k

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Convergence of sum of binomial random variables and central limit theorem

Published on 13 Jul 2014 - 15:22

1.3k

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Distribution of sum of multiplication of i.i.d. exponential random variables.

Published on 03 Aug 2014 - 3:59

102

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Why need triangle arrays in central limit theorem?

Published on 05 Aug 2014 - 6:55

624

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Central Limit Theorem exercise question

Published on 06 Aug 2014 - 18:34

2k

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Central Limit Theorem vs. Weak Law of Large Numbers

Published on 27 Mar 2026 - 15:56

1.1k

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Conditions on Poisson random variables to convergence in probability

Published on 27 Mar 2026 - 2:59

68

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Checking a condition for Central Limit Theorem

Published on 14 Aug 2014 - 3:01

789

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"Practical" Claim about Hypothesis Testing of Bernoulli Distribution Parameter

Published on 27 Mar 2026 - 11:52

138

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Does negative part of a standardized random variable converge to negative part of a $\mathcal{N}(0,1)$?

Published on 21 Aug 2014 - 7:15

List Question

Approximate distribution for the sample mean?

"Show experimentally" that for large $N$, $X$ appears to be normally distributed.

Use central limit theorem to find variance

if $X_i$ are iid standard normal distributed, what is the limiting distribution of $\sum X^4 / (\sum X^2)^2$?

Central Limit Theorem not valid?

Show $\lim_{n\to\infty}\sqrt{n}\bigg(\frac{\sum_{j=1}^{n}X_j}{\sum_{j=1}^{n}X_j^2}\bigg)=Z$

Convergence of sum of binomial random variables and central limit theorem

Distribution of sum of multiplication of i.i.d. exponential random variables.

Why need triangle arrays in central limit theorem?

Central Limit Theorem exercise question

Central Limit Theorem vs. Weak Law of Large Numbers

Conditions on Poisson random variables to convergence in probability

Checking a condition for Central Limit Theorem

"Practical" Claim about Hypothesis Testing of Bernoulli Distribution Parameter

Does negative part of a standardized random variable converge to negative part of a $\mathcal{N}(0,1)$?

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