List questions from conditional-expectation

457

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Proving if $X$ if an $\mathcal{F}$ measurable Random variable with $E(X) < \infty$, then $E(X\mid \mathcal{F}) = X$ a.e.

Published on 03 Nov 2016 - 4:59

1.4k

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Conditional Variance equals zero

Published on 31 Mar 2026 - 12:10

78

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Singular Measures on product $L^2$ Space

Published on 23 Feb 2026 - 4:16

53

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Conditioning a conditional expectation at the initial time point

Published on 30 Mar 2026 - 1:44

2.3k

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A dominated convergence theorem for the conditional expectation $E( \cdot \mid \mathcal{F}_n)$ where $\mathcal{F}_n$ loses information over time

Published on 04 Nov 2016 - 16:13

368

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Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$

Published on 30 Mar 2026 - 8:15

23

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Query related to the average number of children that can buy a toy

Published on 01 Apr 2026 - 5:05

210

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How to decompose this conditional expectation?

Published on 07 Nov 2016 - 6:13

75

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Showing a property of a martingale

Published on 01 Apr 2026 - 20:54

143

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Conditional expectation wrt random variable

Published on 10 Nov 2016 - 12:43

147

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Conditional Expectation for a Joint PMF

Published on 10 Nov 2016 - 15:45

426

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Conditional and Joint Density of Dependent Random Variables

Published on 31 Mar 2026 - 8:30

930

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Conditioning on Brownian motion when $t\in[0,s)$

Published on 11 Nov 2016 - 10:29

3.9k

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Conditional Expectation Given an Event with Poisson Distribution

Published on 28 Mar 2026 - 3:00

426

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Prove/Disprove $E[X|\mathscr G] = X$ if $X$ is almost surely constant.

Published on 25 Mar 2026 - 20:10

List Question

Proving if $X$ if an $\mathcal{F}$ measurable Random variable with $E(X) < \infty$, then $E(X\mid \mathcal{F}) = X$ a.e.

Conditional Variance equals zero

Singular Measures on product $L^2$ Space

Conditioning a conditional expectation at the initial time point

A dominated convergence theorem for the conditional expectation $E( \cdot \mid \mathcal{F}_n)$ where $\mathcal{F}_n$ loses information over time

Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$

Query related to the average number of children that can buy a toy

How to decompose this conditional expectation?

Showing a property of a martingale

Conditional expectation wrt random variable

Conditional Expectation for a Joint PMF

Conditional and Joint Density of Dependent Random Variables

Conditioning on Brownian motion when $t\in[0,s)$

Conditional Expectation Given an Event with Poisson Distribution

Prove/Disprove $E[X|\mathscr G] = X$ if $X$ is almost surely constant.

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