Question

$\mathbf{P}\left(2<\left|X\right|+\left|Y\right|<3\right)$ where the random variables are independent $N(0,1)$?

score 51 · Answer 1 · 2026-02-23 04:41:44

51

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$\mathbf{P}\left(2<\left|X\right|+\left|Y\right|<3\right)$ where the random variables are independent $N(0,1)$?

Published on 23 Feb 2026 - 4:41

score 126 · Answer 2 · 2020-04-06 07:09:52

126

Views

Integrating shifted Gaussian and a polynomial function

Published on 06 Apr 2020 - 7:09

score 13 · Answer 3 · 2026-03-01 07:01:56

Regarding Gaussian integrals, I'm confused about how you combine completing the square and differentiating under the integral sign.

score 25 · Answer 4 · 2020-04-13 17:02:37

25

Views

Integrating $\int dx \int dy (x-y)^2 xy \exp(-a(x-y)^2)$

Published on 13 Apr 2020 - 17:02

score 117 · Answer 5 · 2026-02-23 06:19:41

117

Views

Gaussian integral $\int\limits_\mathbb{R}e^{-\lambda x^{2}} x^2 dx = (\frac{\pi}{4\lambda^3})^\frac{1}{2}$

Published on 23 Feb 2026 - 6:19

score 480 · Answer 6 · 2020-04-15 17:00:38

480

Views

Polar Coordinate Transformation - Motivation

Published on 15 Apr 2020 - 17:00

score 454 · Answer 7 · 2026-02-23 06:18:19

454

Views

Generic integral for n-th order gaussian

Published on 23 Feb 2026 - 6:18

score 58 · Answer 8 · 2020-04-19 18:29:51

58

Views

Minimum value of $2(1-t^2)(1-\Phi(\sqrt{n} t)) + t^2$ for $t \in [0, 1]$ and large $n \ge 3$

Published on 19 Apr 2020 - 18:29

score 329 · Answer 9 · 2020-04-20 20:23:20

329

Views

Is there a way to calculate the improper integral of $e^{-x^2}$ without the use of double integrals?

Published on 20 Apr 2020 - 20:23

score 18 · Answer 10 · 2026-02-23 06:24:19

18

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Find standard deviation $s$ such that $\mathbb{P}(X \in [-t, t]) = 1 - \alpha$ for $X \sim \mathcal{N}(0, s)$

Published on 23 Feb 2026 - 6:24

score 41 · Answer 11 · 2020-04-28 02:22:22

Average of $ \lim_{a \to -\infty} \int_a^\mu \frac{1}{\sigma\sqrt{2\pi}(\mu-a)} \exp \left(-\left(\frac{z-\mu}{\sqrt{2}\sigma}\right)^2\right)\,dz $

score 312 · Answer 12 · 2026-02-23 06:25:24

312

Views

Integral of $\int_{-\infty}^{\infty} \, \cos^{2}(\theta) f_{\Theta}(\theta) \, d\theta$

Published on 23 Feb 2026 - 6:25

score 57 · Answer 13 · 2020-04-30 23:49:18

57

Views

Doubt about the classical way to solve the gaussian integral

Published on 30 Apr 2020 - 23:49

score 411 · Answer 14 · 2020-05-02 10:51:42

411

Views

Real Gaussian integral with complex poles

Published on 02 May 2020 - 10:51

score 106 · Answer 15 · 2020-05-03 10:01:32

106

Views

How to evaluate integral: $ \int_{-\infty}^{\infty} x^{n} e^{-\alpha x^{2}} dx $ only using methods of multidimensional integration

Published on 03 May 2020 - 10:01

List Question

$\mathbf{P}\left(2<\left|X\right|+\left|Y\right|<3\right)$ where the random variables are independent $N(0,1)$?

Integrating shifted Gaussian and a polynomial function

Regarding Gaussian integrals, I'm confused about how you combine completing the square and differentiating under the integral sign.

Integrating $\int dx \int dy (x-y)^2 xy \exp(-a(x-y)^2)$

Gaussian integral $\int\limits_\mathbb{R}e^{-\lambda x^{2}} x^2 dx = (\frac{\pi}{4\lambda^3})^\frac{1}{2}$

Polar Coordinate Transformation - Motivation

Generic integral for n-th order gaussian

Minimum value of $2(1-t^2)(1-\Phi(\sqrt{n} t)) + t^2$ for $t \in [0, 1]$ and large $n \ge 3$

Is there a way to calculate the improper integral of $e^{-x^2}$ without the use of double integrals?

Find standard deviation $s$ such that $\mathbb{P}(X \in [-t, t]) = 1 - \alpha$ for $X \sim \mathcal{N}(0, s)$

Average of $ \lim_{a \to -\infty} \int_a^\mu \frac{1}{\sigma\sqrt{2\pi}(\mu-a)} \exp \left(-\left(\frac{z-\mu}{\sqrt{2}\sigma}\right)^2\right)\,dz $

Integral of $\int_{-\infty}^{\infty} \, \cos^{2}(\theta) f_{\Theta}(\theta) \, d\theta$

Doubt about the classical way to solve the gaussian integral

Real Gaussian integral with complex poles

How to evaluate integral: $ \int_{-\infty}^{\infty} x^{n} e^{-\alpha x^{2}} dx $ only using methods of multidimensional integration

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