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Fundamental properties of conditional expectations

score 35 · Answer 1 · 2026-03-25 23:08:00

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Fundamental properties of conditional expectations

Published on 25 Mar 2026 - 23:08

score 35 · Answer 2 · 2019-09-30 13:19:59

35

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$\phi(x,{}\cdot{})$ independent of $\mathcal{G}\subset \mathcal{F}$. Calculate $\mathbb{E}[\phi(X,\omega)\mid\mathcal{G}]$

Published on 30 Sep 2019 - 13:19

score 409 · Answer 3 · 2026-03-28 14:26:00

409

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Bound on Expectation and Variance of Random variables ratio with positive weights

Published on 28 Mar 2026 - 14:26

score 262 · Answer 4 · 2014-04-10 08:53:39

262

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Compute $E[X \mid Y]$, $E[X]$ and $E[XY^2]$, knowing the distributions of $Y$ and of $X$ conditionally on $Y$

Published on 10 Apr 2014 - 8:53

score 342 · Answer 5 · 2014-04-10 12:59:58

342

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Let $N_n$ be the number of throws before all $n$ dice have shown $6$. Set $m_n := E[N_n]$. Write a recursive formula for $m_n$.

Published on 10 Apr 2014 - 12:59

score 5.8k · Answer 6 · 2014-06-10 21:14:34

5.8k

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Conditional Expectation of X given X^2

Published on 10 Jun 2014 - 21:14

score 195 · Answer 7 · 2026-03-29 15:16:55

195

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Preliminaries of the Martingale Representation Theorem

Published on 29 Mar 2026 - 15:16

score 264 · Answer 8 · 2026-03-29 11:00:55

264

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Conditional expectation onto maximal abelian subalgebras

Published on 29 Mar 2026 - 11:00

score 1.2k · Answer 9 · 2014-07-20 04:31:15

1.2k

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What is the difference between $E[X\mid Y]$ vs $E[X\mid Y=y]$ and some of the properties of $E[X \mid Y]$?

Published on 20 Jul 2014 - 4:31

score 385 · Answer 10 · 2014-07-30 20:36:15

385

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How to show that measurable functions preserve mean independence?

Published on 30 Jul 2014 - 20:36

score 633 · Answer 11 · 2026-03-29 07:21:02

633

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E[X] and E[X^2] with Conditional Expectation

Published on 29 Mar 2026 - 7:21

score 69 · Answer 12 · 2014-08-02 14:08:27

69

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Computing $E(X+U|X)$ where $X$ is Bernoulli and $U$ normal

Published on 02 Aug 2014 - 14:08

score 286 · Answer 13 · 2014-08-03 13:29:15

286

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Compute expectation using tower property

Published on 03 Aug 2014 - 13:29

score 1.1k · Answer 14 · 2014-08-05 12:23:36

1.1k

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The existence of conditional expectation with respect to a sub-$\sigma$-algebra

Published on 05 Aug 2014 - 12:23

score 110 · Answer 15 · 2014-08-07 09:28:09

110

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Law of total expectation: $\mathbb{E}( X | A )$ and $p_{A|B}(a|b)$

Published on 07 Aug 2014 - 9:28

List Question

Fundamental properties of conditional expectations

$\phi(x,{}\cdot{})$ independent of $\mathcal{G}\subset \mathcal{F}$. Calculate $\mathbb{E}[\phi(X,\omega)\mid\mathcal{G}]$

Bound on Expectation and Variance of Random variables ratio with positive weights

Compute $E[X \mid Y]$, $E[X]$ and $E[XY^2]$, knowing the distributions of $Y$ and of $X$ conditionally on $Y$

Let $N_n$ be the number of throws before all $n$ dice have shown $6$. Set $m_n := E[N_n]$. Write a recursive formula for $m_n$.

Conditional Expectation of X given X^2

Preliminaries of the Martingale Representation Theorem

Conditional expectation onto maximal abelian subalgebras

What is the difference between $E[X\mid Y]$ vs $E[X\mid Y=y]$ and some of the properties of $E[X \mid Y]$?

How to show that measurable functions preserve mean independence?

E[X] and E[X^2] with Conditional Expectation

Computing $E(X+U|X)$ where $X$ is Bernoulli and $U$ normal

Compute expectation using tower property

The existence of conditional expectation with respect to a sub-$\sigma$-algebra

Law of total expectation: $\mathbb{E}( X | A )$ and $p_{A|B}(a|b)$

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