Question

Relationship between law of large numbers and regression to the mean

score 137 · Answer 1 · 2026-04-11 11:58:50

137

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Relationship between law of large numbers and regression to the mean

Published on 11 Apr 2026 - 11:58

score 107 · Answer 2 · 2026-04-14 13:03:44

107

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"The proportion of heads after n flips will almost surely converge to 1⁄2 as n approaches infinity."

Published on 14 Apr 2026 - 13:03

score 346 · Answer 3 · 2026-04-10 22:09:08

346

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strong law of large numbers when mean goes to infinity

Published on 10 Apr 2026 - 22:09

score 154 · Answer 4 · 2026-04-14 04:20:24

154

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A doubt about "infinitely often" and $\limsup$ of a sequence (Example of Kai Lai Chung page: 119) without zero-one laws

Published on 14 Apr 2026 - 4:20

score 22 · Answer 5 · 2026-04-15 10:53:30

22

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 15 Apr 2026 - 10:53

score 363 · Answer 6 · 2026-04-10 14:32:02

363

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Problem in convergence in probability involving Poisson distribution.

Published on 10 Apr 2026 - 14:32

score 107 · Answer 7 · 2026-04-14 00:56:35

107

Views

Meaning of the convergence of the sum of a sequence of random variables to a constant

Published on 14 Apr 2026 - 0:56

score 44 · Answer 8 · 2026-04-14 17:55:48

44

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Mutually Independent Events and Expectation and SLLN Diverge

Published on 14 Apr 2026 - 17:55

score 123 · Answer 9 · 2026-04-12 03:11:02

123

Views

Proof verification: Using Chebyshev inequality and weak law of large numbers.

Published on 12 Apr 2026 - 3:11

score 57 · Answer 10 · 2026-04-15 03:01:18

57

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Weak Law of Large Numbers for non independent sequence

Published on 15 Apr 2026 - 3:01

score 75 · Answer 11 · 2026-04-16 14:05:26

75

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Does $\mathbb{P}(X_1 > a) \leq \delta$ imply $\mathbb{P}\left (\frac{1}{J} \sum_{i=1}^J X_i > a \right ) \leq \delta$?

Published on 16 Apr 2026 - 14:05

score 55 · Answer 12 · 2026-04-11 18:47:49

55

Views

Does averaging of random variables always improve concentration?

Published on 11 Apr 2026 - 18:47

score 50 · Answer 13 · 2026-04-16 23:18:03

Difference between $\lim_{n \rightarrow \infty} P(|\bar{X} - \mu| \geq \epsilon) = 0$ and $P(\lim_{n\rightarrow 1} \bar{X} = \mu) = 1$

score 506 · Answer 14 · 2026-04-13 05:02:42

506

Views

Example where law of large numbers does not hold

Published on 13 Apr 2026 - 5:02

score 1k · Answer 15 · 2026-04-12 14:06:50

1k

Views

A Law of Large Numbers for Conditional Expectations

Published on 12 Apr 2026 - 14:06

List Question

Relationship between law of large numbers and regression to the mean

"The proportion of heads after n flips will almost surely converge to 1⁄2 as n approaches infinity."

strong law of large numbers when mean goes to infinity

A doubt about "infinitely often" and $\limsup$ of a sequence (Example of Kai Lai Chung page: 119) without zero-one laws

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

Problem in convergence in probability involving Poisson distribution.

Meaning of the convergence of the sum of a sequence of random variables to a constant

Mutually Independent Events and Expectation and SLLN Diverge

Proof verification: Using Chebyshev inequality and weak law of large numbers.

Weak Law of Large Numbers for non independent sequence

Does $\mathbb{P}(X_1 > a) \leq \delta$ imply $\mathbb{P}\left (\frac{1}{J} \sum_{i=1}^J X_i > a \right ) \leq \delta$?

Does averaging of random variables always improve concentration?

Difference between $\lim_{n \rightarrow \infty} P(|\bar{X} - \mu| \geq \epsilon) = 0$ and $P(\lim_{n\rightarrow 1} \bar{X} = \mu) = 1$

Example where law of large numbers does not hold

A Law of Large Numbers for Conditional Expectations

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