Question

Since the normal distribution is symmetric, why wouldn't $Z$ equal $\sqrt{y}$ and $-\sqrt{y}$ with equal probabilities?

score 57 · Answer 1 · 2026-04-02 06:30:16

57

Views

Since the normal distribution is symmetric, why wouldn't $Z$ equal $\sqrt{y}$ and $-\sqrt{y}$ with equal probabilities?

Published on 02 Apr 2026 - 6:30

score 107 · Answer 2 · 2026-04-02 09:57:09

107

Views

Proof regarding expected value on a Normal Distribution

Published on 02 Apr 2026 - 9:57

score 51 · Answer 3 · 2019-10-17 02:29:09

51

Views

Bounding 4th moments of multivariate normal distribution

Published on 17 Oct 2019 - 2:29

score 69 · Answer 4 · 2019-10-17 04:33:52

69

Views

First coordinate of a randomly chosen point in an Euclidean ball.

Published on 17 Oct 2019 - 4:33

score 632 · Answer 5 · 2019-10-17 11:57:14

632

Views

Expected Value of Continuous Random Variable over Finite Limits

Published on 17 Oct 2019 - 11:57

score 48 · Answer 6 · 2019-10-17 14:03:52

48

Views

Prove $E\left[\mathbf g(\mathbf x)(\mathbf x- \mathbf m)^\intercal\right]=E\left[\mathbf G_{\mathbf x}(\mathbf x)\right]\mathbf P$ for Gaussian x

Published on 17 Oct 2019 - 14:03

score 89 · Answer 7 · 2026-03-28 03:01:06

89

Views

Dimensionality and functional form of the natural conjugate prior to the two-parameter Normal distribution

Published on 28 Mar 2026 - 3:01

score 26 · Answer 8 · 2026-03-25 06:57:31

26

Views

Error Propagation confusion

Published on 25 Mar 2026 - 6:57

score 49 · Answer 9 · 2026-03-29 23:29:05

49

Views

Co-variance of two dependent Gaussian variables

Published on 29 Mar 2026 - 23:29

score 32 · Answer 10 · 2026-04-02 11:40:39

32

Views

$X_1,\cdots,X_5$ is a random sample, $\sim N(0,1)$. Let $T=\sum\limits_{i=1}^5 (X_i-\bar{X})^2$. Find $E(T^2\bar{X}^2)$

Published on 02 Apr 2026 - 11:40

score 2.2k · Answer 11 · 2019-10-21 13:33:48

2.2k

Views

Deriving Mean and Variance of (constant * Gaussian Random Variable) and (constant + Gaussian Random Variable)

Published on 21 Oct 2019 - 13:33

score 26 · Answer 12 · 2019-10-21 14:08:58

26

Views

Symmetric distribution of a Gaussian process

Published on 21 Oct 2019 - 14:08

score 387 · Answer 13 · 2019-10-22 14:59:39

387

Views

$(X, Y)$ is not Bivariate Normal because $P(X + Y = 0) = P(S = −1) = 1/2$, which implies that $X + Y$ can’t be Normal

Published on 22 Oct 2019 - 14:59

score 1.6k · Answer 14 · 2026-04-02 08:09:47

1.6k

Views

Let $X$, $Y$ i.i.d. $\sim \text{N}(0, 1)$. Find the joint distribution of $(X + Y, X − Y)$

Published on 02 Apr 2026 - 8:09

score 2.2k · Answer 15 · 2019-10-23 15:10:25

2.2k

Views

Sum of $n$ correlated normal random variables

Published on 23 Oct 2019 - 15:10

List Question

Since the normal distribution is symmetric, why wouldn't $Z$ equal $\sqrt{y}$ and $-\sqrt{y}$ with equal probabilities?

Proof regarding expected value on a Normal Distribution

Bounding 4th moments of multivariate normal distribution

First coordinate of a randomly chosen point in an Euclidean ball.

Expected Value of Continuous Random Variable over Finite Limits

Prove $E\left[\mathbf g(\mathbf x)(\mathbf x- \mathbf m)^\intercal\right]=E\left[\mathbf G_{\mathbf x}(\mathbf x)\right]\mathbf P$ for Gaussian x

Dimensionality and functional form of the natural conjugate prior to the two-parameter Normal distribution

Error Propagation confusion

Co-variance of two dependent Gaussian variables

$X_1,\cdots,X_5$ is a random sample, $\sim N(0,1)$. Let $T=\sum\limits_{i=1}^5 (X_i-\bar{X})^2$. Find $E(T^2\bar{X}^2)$

Deriving Mean and Variance of (constant * Gaussian Random Variable) and (constant + Gaussian Random Variable)

Symmetric distribution of a Gaussian process

$(X, Y)$ is not Bivariate Normal because $P(X + Y = 0) = P(S = −1) = 1/2$, which implies that $X + Y$ can’t be Normal

Let $X$, $Y$ i.i.d. $\sim \text{N}(0, 1)$. Find the joint distribution of $(X + Y, X − Y)$

Sum of $n$ correlated normal random variables

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