Question

If $f$ is a density function of $\xi$, is there any way to express $\int_{\mathbb{R}}f(x)^2 dx$ in terms of the expected value of $\xi$?

score 57 · Answer 1 · 2026-04-11 02:34:28

57

Views

If $f$ is a density function of $\xi$, is there any way to express $\int_{\mathbb{R}}f(x)^2 dx$ in terms of the expected value of $\xi$?

Published on 11 Apr 2026 - 2:34

score 72 · Answer 2 · 2026-04-11 01:28:43

72

Views

Independence of sigma algebra generated by union of sigma algebra

Published on 11 Apr 2026 - 1:28

score 278 · Answer 3 · 2026-04-09 06:08:38

Prove $\{(\omega,y) \in \Omega \times [0,\infty) \ | \ y \leqslant f(\omega) \}$ is in the product $\sigma$-algebra $\mathcal{A} \otimes \mathcal{B}$

score 264 · Answer 4 · 2026-03-25 00:01:12

264

Views

I have some unclear things in mind related to integrating a Dirichlet function.

Published on 25 Mar 2026 - 0:01

score 456 · Answer 5 · 2026-04-09 02:26:32

456

Views

Extension of Luzin N-property of absolutely continuous functions and measure preserving mappings

Published on 09 Apr 2026 - 2:26

score 165 · Answer 6 · 2026-04-11 21:57:50

165

Views

Martingale Convergence Theorem rational numbers

Published on 11 Apr 2026 - 21:57

score 140 · Answer 7 · 2018-02-01 16:13:18

140

Views

Dominated convergence theorem: Each $f_n$ have to be integrable in the assumption?

Published on 01 Feb 2018 - 16:13

score 242 · Answer 8 · 2026-04-11 09:51:55

242

Views

How can be the Dirichlet function continuous in 0?

Published on 11 Apr 2026 - 9:51

score 107 · Answer 9 · 2018-02-01 19:00:46

107

Views

Lusin theorem and axiom of choice

Published on 01 Feb 2018 - 19:00

score 252 · Answer 10 · 2026-04-09 02:26:32

252

Views

Let $\mu$ be a finite measure on $(X, M)$, and let $\mu^*$ be the outermeasure induced by $\mu$.

Published on 09 Apr 2026 - 2:26

score 107 · Answer 11 · 2026-03-25 01:20:28

107

Views

Evaluate $\lim_{n\to\infty} \int_{n}^{\infty}\frac{n^2\arctan(x)\arctan(\frac{1}{x})}{n^2+x^2}$

Published on 25 Mar 2026 - 1:20

score 78 · Answer 12 · 2018-02-02 02:45:09

78

Views

$E(X)=\int_0^{\infty} (1-F(t)) dt-\int_{\infty}^0 F(t) dt$?

Published on 02 Feb 2018 - 2:45

score 131 · Answer 13 · 2018-02-02 04:55:33

131

Views

Are there $\sigma$-rings countable?

Published on 02 Feb 2018 - 4:55

score 3.4k · Answer 14 · 2026-04-11 09:19:45

3.4k

Views

A confusion about the definition of Jordan measurable set

Published on 11 Apr 2026 - 9:19

score 77 · Answer 15 · 2026-03-25 03:02:40

77

Views

Let $E \subseteq \mathbb{R}^n$, and $f \in R(E)$, then is the fact that $f$ is continuous on $E$ implies $\mu(E) > 0$?

Published on 25 Mar 2026 - 3:02

List Question

If $f$ is a density function of $\xi$, is there any way to express $\int_{\mathbb{R}}f(x)^2 dx$ in terms of the expected value of $\xi$?

Independence of sigma algebra generated by union of sigma algebra

Prove $\{(\omega,y) \in \Omega \times [0,\infty) \ | \ y \leqslant f(\omega) \}$ is in the product $\sigma$-algebra $\mathcal{A} \otimes \mathcal{B}$

I have some unclear things in mind related to integrating a Dirichlet function.

Extension of Luzin N-property of absolutely continuous functions and measure preserving mappings

Martingale Convergence Theorem rational numbers

Dominated convergence theorem: Each $f_n$ have to be integrable in the assumption?

How can be the Dirichlet function continuous in 0?

Lusin theorem and axiom of choice

Let $\mu$ be a finite measure on $(X, M)$, and let $\mu^*$ be the outermeasure induced by $\mu$.

Evaluate $\lim_{n\to\infty} \int_{n}^{\infty}\frac{n^2\arctan(x)\arctan(\frac{1}{x})}{n^2+x^2}$

$E(X)=\int_0^{\infty} (1-F(t)) dt-\int_{\infty}^0 F(t) dt$?

Are there $\sigma$-rings countable?

A confusion about the definition of Jordan measurable set

Let $E \subseteq \mathbb{R}^n$, and $f \in R(E)$, then is the fact that $f$ is continuous on $E$ implies $\mu(E) > 0$?

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