Question

Calculating variance upon removing a value from the sample

score 402 · Answer 1 · 2016-05-30 23:13:49

402

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Calculating variance upon removing a value from the sample

Published on 30 May 2016 - 23:13

score 300 · Answer 2 · 2016-06-01 07:39:12

300

Views

If $Var(X)\leq 1/2$, prove that $P(E(X)-1\leq X\leq 2E(X))\geq 1/2$.

Published on 01 Jun 2016 - 7:39

score 43 · Answer 3 · 2016-06-01 22:39:34

43

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Convergence and power means

Published on 01 Jun 2016 - 22:39

score 172 · Answer 4 · 2016-06-03 09:14:54

172

Views

How does $(\sqrt{xy}+\sqrt{yz}+\sqrt{zx})/3$ relate to $\sqrt[3]{xyz}$ for $x,y,z>0$?

Published on 03 Jun 2016 - 9:14

score 268 · Answer 5 · 2026-03-30 06:48:46

268

Views

How does $\sqrt{x^2+y^2}+\sqrt{y^2+z^2}+\sqrt{z^2+x^2}$ relate to $\sqrt{x^2+y^2+z^2}$?

Published on 30 Mar 2026 - 6:48

score 257 · Answer 6 · 2026-03-30 12:40:11

257

Views

Extending the ordered sequence of 'three-number means' beyond AM, GM and HM

Published on 30 Mar 2026 - 12:40

score 240 · Answer 7 · 2016-06-04 10:31:15

How $2 \sqrt[3]{\frac{x^2y^2z^2}{(x+y)(y+z)(z+x)}}$ and $\frac{3xyz}{x\sqrt{yz}+y\sqrt{zx}+z\sqrt{xy}}$ are related for $x,y,z \geq 0$?

score 1.7k · Answer 8 · 2016-06-04 18:05:54

1.7k

Views

Prove $\frac{\sqrt[3]{(x+y)(y+z)(z+x)}}{2} \geq \sqrt{\frac{xy+yz+zx}{3}}$ for $x,y,z \geq 0$

Published on 04 Jun 2016 - 18:05

score 159 · Answer 9 · 2016-06-05 14:09:17

Prove $\frac{\sqrt{x^2+y^2}+\sqrt{y^2+z^2}+\sqrt{z^2+x^2}}{3 \sqrt{2}} \geq \frac{\sqrt{(x+y)^2+(y+z)^2+(z+x)^2}}{2 \sqrt{3}}$ for $x,y,z \geq 0$

score 1.2k · Answer 10 · 2016-06-06 06:31:10

1.2k

Views

Prove $\frac{3\sqrt{xyz}}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \frac{2}{3} \left(\frac{xy}{x+y}+\frac{yz}{y+z}+\frac{zx}{z+x} \right)$ for $x,y,z \geq 0$

Published on 06 Jun 2016 - 6:31

score 331 · Answer 11 · 2016-06-11 21:48:14

331

Views

A new type of Arithmetic-Harmonic mean for $n$ numbers

Published on 11 Jun 2016 - 21:48

score 465 · Answer 12 · 2016-06-12 08:16:53

465

Views

Computing cube roots using three number means

Published on 12 Jun 2016 - 8:16

score 547 · Answer 13 · 2016-06-13 09:54:31

547

Views

Calculating the average with Limited memory and without using the count

Published on 13 Jun 2016 - 9:54

score 249 · Answer 14 · 2016-06-14 10:33:24

249

Views

Limit and rate of convergence of the sequence $a_{n+1}=\frac{a_n^2+b_n^2}{a_n+b_n},~~b_{n+1}=\frac{a_n+b_n}{2}$

Published on 14 Jun 2016 - 10:33

score 203 · Answer 15 · 2016-06-14 13:19:39

203

Views

Prove an algorithm for logarithmic mean $\lim_{n \to \infty} a_n=\lim_{n \to \infty} b_n=\frac{a_0-b_0}{\ln a_0-\ln b_0}$

Published on 14 Jun 2016 - 13:19

List Question

Calculating variance upon removing a value from the sample

If $Var(X)\leq 1/2$, prove that $P(E(X)-1\leq X\leq 2E(X))\geq 1/2$.

Convergence and power means

How does $(\sqrt{xy}+\sqrt{yz}+\sqrt{zx})/3$ relate to $\sqrt[3]{xyz}$ for $x,y,z>0$?

How does $\sqrt{x^2+y^2}+\sqrt{y^2+z^2}+\sqrt{z^2+x^2}$ relate to $\sqrt{x^2+y^2+z^2}$?

Extending the ordered sequence of 'three-number means' beyond AM, GM and HM

How $2 \sqrt[3]{\frac{x^2y^2z^2}{(x+y)(y+z)(z+x)}}$ and $\frac{3xyz}{x\sqrt{yz}+y\sqrt{zx}+z\sqrt{xy}}$ are related for $x,y,z \geq 0$?

Prove $\frac{\sqrt[3]{(x+y)(y+z)(z+x)}}{2} \geq \sqrt{\frac{xy+yz+zx}{3}}$ for $x,y,z \geq 0$

Prove $\frac{\sqrt{x^2+y^2}+\sqrt{y^2+z^2}+\sqrt{z^2+x^2}}{3 \sqrt{2}} \geq \frac{\sqrt{(x+y)^2+(y+z)^2+(z+x)^2}}{2 \sqrt{3}}$ for $x,y,z \geq 0$

Prove $\frac{3\sqrt{xyz}}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \frac{2}{3} \left(\frac{xy}{x+y}+\frac{yz}{y+z}+\frac{zx}{z+x} \right)$ for $x,y,z \geq 0$

A new type of Arithmetic-Harmonic mean for $n$ numbers

Computing cube roots using three number means

Calculating the average with Limited memory and without using the count

Limit and rate of convergence of the sequence $a_{n+1}=\frac{a_n^2+b_n^2}{a_n+b_n},~~b_{n+1}=\frac{a_n+b_n}{2}$

Prove an algorithm for logarithmic mean $\lim_{n \to \infty} a_n=\lim_{n \to \infty} b_n=\frac{a_0-b_0}{\ln a_0-\ln b_0}$

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