Question

Find the conditional distribution of $X_t$ given $X_t+Y_t=n $ , and find $\Bbb{E}[X_t+Y_t|X_{2t}]$.

score 149 · Answer 1 · 2026-03-26 06:32:41

149

Views

Find the conditional distribution of $X_t$ given $X_t+Y_t=n $ , and find $\Bbb{E}[X_t+Y_t|X_{2t}]$.

Published on 26 Mar 2026 - 6:32

score 72 · Answer 2 · 2019-03-26 19:37:01

72

Views

Random Variable convergence in $L^{q}$ space, then the conditional expectation also converges in $L^{q}$

Published on 26 Mar 2019 - 19:37

score 155 · Answer 3 · 2026-03-28 07:57:23

155

Views

Given $\mathbb E(5X+2)=12$ and $\mathbb E(X|Y)=Y^3$ compute $\mathbb E(Y^3)$

Published on 28 Mar 2026 - 7:57

score 497 · Answer 4 · 2026-03-28 02:48:36

497

Views

Application of Lévy Zero-One Law

Published on 28 Mar 2026 - 2:48

score 41 · Answer 5 · 2019-03-29 02:05:20

41

Views

If $Y_n=E(X|\mathcal{F}_n)$ for some $\mathcal{F}_n \subset \mathcal{F}$ and if $Y_n \to Y$ with probability one. Show $Y_n \to Y$ in $L^1$.

Published on 29 Mar 2019 - 2:05

score 180 · Answer 6 · 2026-03-28 09:45:37

180

Views

How to find the optimal decoder that minimizes the probability of error?

Published on 28 Mar 2026 - 9:45

score 1.2k · Answer 7 · 2019-03-29 21:56:17

1.2k

Views

Convergence in $L_1$ of conditional expectation.

Published on 29 Mar 2019 - 21:56

score 72 · Answer 8 · 2019-03-30 17:04:46

72

Views

Discrete random variable-expected value

Published on 30 Mar 2019 - 17:04

score 235 · Answer 9 · 2026-03-28 09:54:16

235

Views

The exercise from L. Breiman " Probability " page 76

Published on 28 Mar 2026 - 9:54

score 76 · Answer 10 · 2019-03-31 08:35:16

76

Views

What does it mean $\mathbb E[\Phi(x,Y)]|_{x=X}$ in the book of R. Schilling (Brownian motion)?

Published on 31 Mar 2019 - 8:35

score 30 · Answer 11 · 2026-03-26 20:41:14

30

Views

Why $\mathbb P\{X_v\in A\mid \mathcal F_s\}=\int P_{s,t}(X_s,dy)P_{t,v}(y,A)$?

Published on 26 Mar 2026 - 20:41

score 1.7k · Answer 12 · 2026-02-23 08:24:26

1.7k

Views

Proof of an Abstract Bayes' Theorem

Published on 23 Feb 2026 - 8:24

score 35 · Answer 13 · 2019-03-31 21:55:44

35

Views

How to approximate a Mixture distribution by a single distribution

Published on 31 Mar 2019 - 21:55

score 118 · Answer 14 · 2019-04-01 12:16:39

118

Views

Show that this integral function is a version of the expected value.

Published on 01 Apr 2019 - 12:16

score 69 · Answer 15 · 2026-03-28 09:54:18

69

Views

Measurability when conditioning on a sub-sigma field

Published on 28 Mar 2026 - 9:54

List Question

Find the conditional distribution of $X_t$ given $X_t+Y_t=n $ , and find $\Bbb{E}[X_t+Y_t|X_{2t}]$.

Random Variable convergence in $L^{q}$ space, then the conditional expectation also converges in $L^{q}$

Given $\mathbb E(5X+2)=12$ and $\mathbb E(X|Y)=Y^3$ compute $\mathbb E(Y^3)$

Application of Lévy Zero-One Law

If $Y_n=E(X|\mathcal{F}_n)$ for some $\mathcal{F}_n \subset \mathcal{F}$ and if $Y_n \to Y$ with probability one. Show $Y_n \to Y$ in $L^1$.

How to find the optimal decoder that minimizes the probability of error?

Convergence in $L_1$ of conditional expectation.

Discrete random variable-expected value

The exercise from L. Breiman " Probability " page 76

What does it mean $\mathbb E[\Phi(x,Y)]|_{x=X}$ in the book of R. Schilling (Brownian motion)?

Why $\mathbb P\{X_v\in A\mid \mathcal F_s\}=\int P_{s,t}(X_s,dy)P_{t,v}(y,A)$?

Proof of an Abstract Bayes' Theorem

How to approximate a Mixture distribution by a single distribution

Show that this integral function is a version of the expected value.

Measurability when conditioning on a sub-sigma field

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