Question

If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $\lim_{k \to \infty} E[X\mid\mathcal{F}_k]=E[X\mid\mathcal{W}]$ a.s?

score 112 · Answer 1 · 2026-04-15 19:48:08

112

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If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $\lim_{k \to \infty} E[X\mid\mathcal{F}_k]=E[X\mid\mathcal{W}]$ a.s?

Published on 15 Apr 2026 - 19:48

score 158 · Answer 2 · 2026-04-13 01:08:27

158

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Transformation of sub-martingale and super-martingale

Published on 13 Apr 2026 - 1:08

score 37 · Answer 3 · 2026-04-12 16:41:00

37

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If $\mathbb{E}[X|Y] =X$ for $X,Y$ Gaussian, what is $p(x|y)$?

Published on 12 Apr 2026 - 16:41

score 2.2k · Answer 4 · 2026-04-08 20:55:36

2.2k

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score 50 · Answer 5 · 2026-04-13 12:18:34

50

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Is this inequality true: $E(A \mid A\leq B) \geq E(A \mid A\leq \min(B,C))$?

Published on 13 Apr 2026 - 12:18

score 94 · Answer 6 · 2026-04-10 16:23:31

94

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Applying Conditional Expectation to Inequality

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score 300 · Answer 7 · 2026-04-14 02:19:59

300

Views

Expected number of cycles for random permutation given that there are at least r cycles

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score 350 · Answer 8 · 2026-04-17 14:47:30

350

Views

Show that $\mathbb{E}(\lim_{n\to\infty} X_n|\mathcal{F}_n)\ge X_n$ for $(X_n)_{n\ge 0}$ a UI submartingale

Published on 17 Apr 2026 - 14:47

score 717 · Answer 9 · 2026-04-10 22:47:58

717

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score 175 · Answer 10 · 2026-04-10 21:08:10

175

Views

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score 178 · Answer 11 · 2026-04-16 16:27:42

178

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Find UMVUE of $\tau=(\lambda-\mu)e^{-(\lambda+\mu)}$ from samples $X_1, \dots, X_n\sim \rm{Pois}(\lambda)$ and $Y_1,\dots, Y_n\sim \rm{Pois}(\mu)$.

Published on 16 Apr 2026 - 16:27

score 446 · Answer 12 · 2026-04-14 14:54:28

446

Views

Conditional independence of random variables and $\mathbf{E}[XY]=\mathbf{E}[X]\cdot\mathbf{E}[Y]$

Published on 14 Apr 2026 - 14:54

score 73 · Answer 13 · 2026-04-11 01:28:20

73

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Published on 11 Apr 2026 - 1:28

score 112 · Answer 14 · 2026-04-13 09:03:27

112

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The mean ergodic theorem for weakly mixing extension

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score 469 · Answer 15 · 2026-04-13 10:00:09

469

Views

Conceptual Issues in the Measure Theoretic Proof of Conditional Expectations (via Radon-Nikodym)

Published on 13 Apr 2026 - 10:00

List Question

If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $\lim_{k \to \infty} E[X\mid\mathcal{F}_k]=E[X\mid\mathcal{W}]$ a.s?

Transformation of sub-martingale and super-martingale

If $\mathbb{E}[X|Y] =X$ for $X,Y$ Gaussian, what is $p(x|y)$?

Probability of Rain Question

Is this inequality true: $E(A \mid A\leq B) \geq E(A \mid A\leq \min(B,C))$?

Applying Conditional Expectation to Inequality

Expected number of cycles for random permutation given that there are at least r cycles

Show that $\mathbb{E}(\lim_{n\to\infty} X_n|\mathcal{F}_n)\ge X_n$ for $(X_n)_{n\ge 0}$ a UI submartingale

A proof for Polya's urn model

Conditional Expectation Example

Find UMVUE of $\tau=(\lambda-\mu)e^{-(\lambda+\mu)}$ from samples $X_1, \dots, X_n\sim \rm{Pois}(\lambda)$ and $Y_1,\dots, Y_n\sim \rm{Pois}(\mu)$.

Conditional independence of random variables and $\mathbf{E}[XY]=\mathbf{E}[X]\cdot\mathbf{E}[Y]$

Simplification of Expected Value Problem

The mean ergodic theorem for weakly mixing extension

Conceptual Issues in the Measure Theoretic Proof of Conditional Expectations (via Radon-Nikodym)

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