Question

Prove that $E\left(\frac{XY}{X^2+Y^2}\right) \geqslant 0$ for i.i.d. $X$ and $Y$

score 527 · Answer 1 · 2017-04-22 18:26:56

527

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Prove that $E\left(\frac{XY}{X^2+Y^2}\right) \geqslant 0$ for i.i.d. $X$ and $Y$

Published on 22 Apr 2017 - 18:26

score 801 · Answer 2 · 2026-04-11 06:59:32

801

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How to calculate probability that a random variable is less than the max of two other random variables?

Published on 11 Apr 2026 - 6:59

score 44 · Answer 3 · 2026-04-12 00:18:19

44

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Convergence of maximum of dependent RVs

Published on 12 Apr 2026 - 0:18

score 2.1k · Answer 4 · 2026-03-25 07:44:47

2.1k

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Expected Revenue of 2nd Price Auction with Reserve Price

Published on 25 Mar 2026 - 7:44

score 6.7k · Answer 5 · 2026-04-09 17:59:52

6.7k

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Density of Gaussian Random variable conditioned on sum

Published on 09 Apr 2026 - 17:59

score 251 · Answer 6 · 2026-04-09 15:31:39

251

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The expectation of the random variable (Poisson process)

Published on 09 Apr 2026 - 15:31

score 46 · Answer 7 · 2026-04-11 19:02:13

46

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What part of the Covariance formula determines its sign?

Published on 11 Apr 2026 - 19:02

score 164 · Answer 8 · 2026-03-30 13:40:30

164

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If $X_1 \rightarrow X_2 \rightarrow X_3 \rightarrow X_4$ is a Markov chain, is $X_2 \rightarrow X_3 \rightarrow X_4$ also one?

Published on 30 Mar 2026 - 13:40

score 673 · Answer 9 · 2026-04-12 07:09:40

673

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Finding the Expected number of steps to absorption for a Martingale based on a simple random walk.

Published on 12 Apr 2026 - 7:09

score 6.5k · Answer 10 · 2017-04-25 12:55:39

6.5k

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Prove that $\Bbb{E}(|X-Y|) \le \Bbb{E}(|X+Y|)$ for i.i.d $X$ and $Y$

Published on 25 Apr 2017 - 12:55

score 36 · Answer 11 · 2026-04-12 06:47:05

36

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Properties of random variables with $E[ \sin(X+Z) \sin(3X+Z)]=0. $

Published on 12 Apr 2026 - 6:47

score 83 · Answer 12 · 2026-04-11 08:55:23

83

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Maximize the result in repeated die rolls

Published on 11 Apr 2026 - 8:55

score 51 · Answer 13 · 2017-04-25 22:01:31

51

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$ \lim_{ \|x\| \to 0 } \frac{E \left[ \log \left(1+ \left(\|x\|^2+ \langle x,Z \rangle \right)^2 \right) \right]}{\| x\|^2} = 1$

Published on 25 Apr 2017 - 22:01

score 538 · Answer 14 · 2026-04-09 04:16:36

538

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Intuitive interpretation on an expectation equation

Published on 09 Apr 2026 - 4:16

score 91 · Answer 15 · 2026-04-11 11:59:59

91

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Expectation of increasing transformation of random variables

Published on 11 Apr 2026 - 11:59

List Question

Prove that $E\left(\frac{XY}{X^2+Y^2}\right) \geqslant 0$ for i.i.d. $X$ and $Y$

How to calculate probability that a random variable is less than the max of two other random variables?

Convergence of maximum of dependent RVs

Expected Revenue of 2nd Price Auction with Reserve Price

Density of Gaussian Random variable conditioned on sum

The expectation of the random variable (Poisson process)

What part of the Covariance formula determines its sign?

If $X_1 \rightarrow X_2 \rightarrow X_3 \rightarrow X_4$ is a Markov chain, is $X_2 \rightarrow X_3 \rightarrow X_4$ also one?

Finding the Expected number of steps to absorption for a Martingale based on a simple random walk.

Prove that $\Bbb{E}(|X-Y|) \le \Bbb{E}(|X+Y|)$ for i.i.d $X$ and $Y$

Properties of random variables with $E[ \sin(X+Z) \sin(3X+Z)]=0. $

Maximize the result in repeated die rolls

$ \lim_{ \|x\| \to 0 } \frac{E \left[ \log \left(1+ \left(\|x\|^2+ \langle x,Z \rangle \right)^2 \right) \right]}{\| x\|^2} = 1$

Intuitive interpretation on an expectation equation

Expectation of increasing transformation of random variables

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