Question

Let $(X,Y)$ be a Gaussian random vector with given means, variances and correlation, determine $E[X\mid X+Y]$ and $E[X\mid Y]$

score 682 · Answer 1 · 2026-04-02 21:50:34

682

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Let $(X,Y)$ be a Gaussian random vector with given means, variances and correlation, determine $E[X\mid X+Y]$ and $E[X\mid Y]$

Published on 02 Apr 2026 - 21:50

score 40 · Answer 2 · 2026-03-25 17:51:52

40

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Relationship (sum/difference) between elements having normal distribution

Published on 25 Mar 2026 - 17:51

score 41 · Answer 3 · 2026-03-29 10:18:27

41

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Example of a set based on random variables

Published on 29 Mar 2026 - 10:18

score 75 · Answer 4 · 2026-03-28 13:30:57

75

Views

iid random samples

Published on 28 Mar 2026 - 13:30

score 466 · Answer 5 · 2020-05-15 15:26:50

466

Views

To prove circularly symmetric Gaussian random variables have iid real and imaginary components

Published on 15 May 2020 - 15:26

score 535 · Answer 6 · 2020-05-15 17:46:19

535

Views

The PDF of the sum of two independent random variables with the normal distribution

Published on 15 May 2020 - 17:46

score 107 · Answer 7 · 2026-03-30 05:26:47

107

Views

Finding pdfs of $\frac1{X^2}$ and $\frac{1}{4}\left(\frac1{X^2}+\frac1{W^2}\right)$ where $X,W$ are independent $N(0,1)$

Published on 30 Mar 2026 - 5:26

score 190 · Answer 8 · 2020-05-16 13:14:13

190

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Finding $\alpha,\beta,\gamma,\delta $ such that $V =\alpha X + \beta Y + \gamma Z + \delta\sim N(0,1) $

Published on 16 May 2020 - 13:14

score 246 · Answer 9 · 2026-03-27 18:08:22

246

Views

Finding joint moment generating function of $Y_1$ and $Y_2$

Published on 27 Mar 2026 - 18:08

score 74 · Answer 10 · 2026-03-26 15:40:18

74

Views

Why this is Normal Distribution?

Published on 26 Mar 2026 - 15:40

score 108 · Answer 11 · 2026-03-25 16:03:24

108

Views

CDF of mixture of Normal standard and Poisson

Published on 25 Mar 2026 - 16:03

score 53 · Answer 12 · 2026-03-25 09:25:46

53

Views

Finding the Joint Distribution of Two Normally Distributed Random Variables

Published on 25 Mar 2026 - 9:25

score 228 · Answer 13 · 2026-03-27 00:10:04

228

Views

Applying the Central Limit Theorem to show $\lim_{N \rightarrow \infty} \mathbb{P}(0 \leq \sqrt{12N}(\overline{X}_n -\frac{1}{2}) \leq 1) = I$

Published on 27 Mar 2026 - 0:10

score 28 · Answer 14 · 2026-03-27 23:32:11

28

Views

Optimal estimators of Gaussian under certain conditions

Published on 27 Mar 2026 - 23:32

score 95 · Answer 15 · 2020-05-20 14:26:42

95

Views

Multivariate Gaussian product derivation

Published on 20 May 2020 - 14:26

List Question

Let $(X,Y)$ be a Gaussian random vector with given means, variances and correlation, determine $E[X\mid X+Y]$ and $E[X\mid Y]$

Relationship (sum/difference) between elements having normal distribution

Example of a set based on random variables

iid random samples

To prove circularly symmetric Gaussian random variables have iid real and imaginary components

The PDF of the sum of two independent random variables with the normal distribution

Finding pdfs of $\frac1{X^2}$ and $\frac{1}{4}\left(\frac1{X^2}+\frac1{W^2}\right)$ where $X,W$ are independent $N(0,1)$

Finding $\alpha,\beta,\gamma,\delta $ such that $V =\alpha X + \beta Y + \gamma Z + \delta\sim N(0,1) $

Finding joint moment generating function of $Y_1$ and $Y_2$

Why this is Normal Distribution?

CDF of mixture of Normal standard and Poisson

Finding the Joint Distribution of Two Normally Distributed Random Variables

Applying the Central Limit Theorem to show $\lim_{N \rightarrow \infty} \mathbb{P}(0 \leq \sqrt{12N}(\overline{X}_n -\frac{1}{2}) \leq 1) = I$

Optimal estimators of Gaussian under certain conditions

Multivariate Gaussian product derivation

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