List questions from conditional-expectation

Published on 01 Apr 2026 - 21:00

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Conditional Expectation of product, where one conditional expectation is already known.

Published on 18 May 2023 - 17:21

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Alternative definitions of regular conditional distribution.

Published on 18 May 2023 - 20:36

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Show that $Var(X| \mathcal{G}) \leq Var(X)$

Published on 21 May 2023 - 2:03

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Finding conditional expectation by definition

Published on 23 May 2023 - 11:57

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If $E|Y|\lt \infty$, $E[Y|X] = m(X)$ and $(X_1,Y_1)$ come from same distribution as $(X,Y)$. Is it true that $E[Y_1|X_1] = m(X_1)$?

Published on 24 May 2023 - 10:27

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In linear regression, is there a formal argument that fixed design is "equivalent" to regressors being independent of random errors?

Published on 28 Mar 2026 - 9:57

55

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Evaluating conditional probability and expectations on event

Published on 25 May 2023 - 12:40

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Is there a quick trick to see $\mathbb{E}[\theta|L=l] = \mathbb{E}_{\Lambda}\left[ \mathbb{E}[\theta|\Lambda, L=l] | L=l \right]$ without expanding?

Published on 25 May 2023 - 21:26

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Equilibrium values in test-taking game

Published on 28 Mar 2026 - 8:38

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How can we compute the following

Published on 29 May 2023 - 13:52

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What is $E(X|XY)$?

Published on 30 May 2023 - 23:38

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Why is this L2 a (closed) subspace of another L2?

Published on 03 Jun 2023 - 13:29

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Notation of Conditional Expectation

Published on 05 Jun 2023 - 1:13

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Joint density function: $f_{X,Y}(x,y) = \frac{x^3}{2} e^{-x(y+1)}$. Find $\mathbb{E} (Y|X)$, $\mathbb{E} (Y^2|X^2)$ and $\mathbb{P} (Y>1|X^3 + 1)$.

Published on 01 Apr 2026 - 5:46

List Question

Definition od essential supremum for martingales with many measures

Conditional Expectation of product, where one conditional expectation is already known.

Alternative definitions of regular conditional distribution.

Show that $Var(X| \mathcal{G}) \leq Var(X)$

Finding conditional expectation by definition

If $E|Y|\lt \infty$, $E[Y|X] = m(X)$ and $(X_1,Y_1)$ come from same distribution as $(X,Y)$. Is it true that $E[Y_1|X_1] = m(X_1)$?

In linear regression, is there a formal argument that fixed design is "equivalent" to regressors being independent of random errors?

Evaluating conditional probability and expectations on event

Is there a quick trick to see $\mathbb{E}[\theta|L=l] = \mathbb{E}_{\Lambda}\left[ \mathbb{E}[\theta|\Lambda, L=l] | L=l \right]$ without expanding?

Equilibrium values in test-taking game

How can we compute the following

What is $E(X|XY)$?

Why is this L2 a (closed) subspace of another L2?

Notation of Conditional Expectation

Joint density function: $f_{X,Y}(x,y) = \frac{x^3}{2} e^{-x(y+1)}$. Find $\mathbb{E} (Y|X)$, $\mathbb{E} (Y^2|X^2)$ and $\mathbb{P} (Y>1|X^3 + 1)$.

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