Question

Sample mean: dependence

score 65 · Answer 1 · 2016-08-04 17:07:51

65

Views

Sample mean: dependence

Published on 04 Aug 2016 - 17:07

score 92 · Answer 2 · 2016-08-07 14:30:18

92

Views

Can these averaging formulas be expressed as transformations of the arithmetic mean?

Published on 07 Aug 2016 - 14:30

score 1.9k · Answer 3 · 2026-03-25 18:49:47

1.9k

Views

Reciprocal of a normal variable with non-zero mean and small variance

Published on 25 Mar 2026 - 18:49

score 97 · Answer 4 · 2016-08-12 19:09:22

97

Views

Inconsistent means when values have high decimal places

Published on 12 Aug 2016 - 19:09

score 87 · Answer 5 · 2016-08-13 23:40:17

87

Views

The concentration rate of the sample mean of the "smallest" samples given the concentration rate over all samples

Published on 13 Aug 2016 - 23:40

score 61 · Answer 6 · 2016-08-16 14:40:06

61

Views

Is mean a mathematical function?

Published on 16 Aug 2016 - 14:40

score 279 · Answer 7 · 2016-08-18 19:44:14

279

Views

Modified AGM: $a_{n+1}=\frac{a_n+b_n}{2}, \quad b_{n+1}=a_n+b_n-\sqrt{a_n b_n}$

Published on 18 Aug 2016 - 19:44

score 69 · Answer 8 · 2016-08-19 22:00:12

69

Views

Expected generations until first mutation (aka, trials to first success with non-constant p)

Published on 19 Aug 2016 - 22:00

score 172 · Answer 9 · 2026-03-25 23:42:22

172

Views

Prove that this family of iterated means gives odd powers of Arithmetic-Geometric Mean in the limit

Published on 25 Mar 2026 - 23:42

score 539 · Answer 10 · 2026-03-26 16:10:15

539

Views

Prove this integral $\int_0^\infty \frac{dx}{\sqrt{x^4+a^4}+\sqrt{x^4+b^4}}=\frac{\Gamma(1/4)^2 }{6 \sqrt{\pi}} \frac{a^3-b^3}{a^4-b^4}$

Published on 26 Mar 2026 - 16:10

score 266 · Answer 11 · 2016-08-25 07:21:46

266

Views

Iterated means $a_{n+1}=\sqrt{a_n \frac{b_n+c_n}{2}}$, $b_{n+1}$ and $c_{n+1}$ similar, closed form for general initial conditions?

Published on 25 Aug 2016 - 7:21

score 2.1k · Answer 12 · 2016-08-25 15:28:01

2.1k

Views

Prove inequality $\arccos \left( \frac{\sin 1-\sin x}{1-x} \right) \leq \sqrt{\frac{1+x+x^2}{3}}$

Published on 25 Aug 2016 - 15:28

score 3.9k · Answer 13 · 2016-08-25 18:56:09

3.9k

Views

Positive number whose square exceeds its cube by the greatest amount

Published on 25 Aug 2016 - 18:56

score 2.3k · Answer 14 · 2026-03-27 03:42:21

2.3k

Views

A near "geometric mean" that handles zeros and negative numbers

Published on 27 Mar 2026 - 3:42

score 622 · Answer 15 · 2026-03-25 20:12:00

622

Views

Prove inequality $\ln \left( \frac{e-e^x}{1-x} \right) \leq \sqrt{\frac{1+x+x^2}{3}}$ for $0<x \le 1$

Published on 25 Mar 2026 - 20:12

List Question

Sample mean: dependence

Can these averaging formulas be expressed as transformations of the arithmetic mean?

Reciprocal of a normal variable with non-zero mean and small variance

Inconsistent means when values have high decimal places

The concentration rate of the sample mean of the "smallest" samples given the concentration rate over all samples

Is mean a mathematical function?

Modified AGM: $a_{n+1}=\frac{a_n+b_n}{2}, \quad b_{n+1}=a_n+b_n-\sqrt{a_n b_n}$

Expected generations until first mutation (aka, trials to first success with non-constant p)

Prove that this family of iterated means gives odd powers of Arithmetic-Geometric Mean in the limit

Prove this integral $\int_0^\infty \frac{dx}{\sqrt{x^4+a^4}+\sqrt{x^4+b^4}}=\frac{\Gamma(1/4)^2 }{6 \sqrt{\pi}} \frac{a^3-b^3}{a^4-b^4}$

Iterated means $a_{n+1}=\sqrt{a_n \frac{b_n+c_n}{2}}$, $b_{n+1}$ and $c_{n+1}$ similar, closed form for general initial conditions?

Prove inequality $\arccos \left( \frac{\sin 1-\sin x}{1-x} \right) \leq \sqrt{\frac{1+x+x^2}{3}}$

Positive number whose square exceeds its cube by the greatest amount

A near "geometric mean" that handles zeros and negative numbers

Prove inequality $\ln \left( \frac{e-e^x}{1-x} \right) \leq \sqrt{\frac{1+x+x^2}{3}}$ for $0<x \le 1$

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