Question

Show that $E[X \mid \sigma (\mathscr{G},\mathscr{H})] = E[X \mid \mathscr{G}]$ if $\mathscr{H}$ independent of $\sigma (\sigma (X),\mathscr{G})$

score 697 · Answer 1 · 2014-09-17 20:39:36

Show that $E[X \mid \sigma (\mathscr{G},\mathscr{H})] = E[X \mid \mathscr{G}]$ if $\mathscr{H}$ independent of $\sigma (\sigma (X),\mathscr{G})$

score 130 · Answer 2 · 2014-09-17 22:48:29

130

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Expectation of a Random Variable multiplied by a Conditonal Expectation.

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score 1.3k · Answer 3 · 2014-09-19 22:58:10

1.3k

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score 93 · Answer 4 · 2014-09-20 15:50:23

93

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Old Notation for Conditional Expectation

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score 245 · Answer 5 · 2014-09-20 21:20:54

245

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Law of total probability in continous case

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score 144 · Answer 6 · 2026-03-29 15:44:18

144

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score 522 · Answer 7 · 2014-09-22 03:27:55

522

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score 527 · Answer 8 · 2026-03-29 15:42:12

527

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Definition and derivation of conditional expectation/probability

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score 461 · Answer 9 · 2026-03-25 14:18:27

461

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conditional expected value - Poisson process plus random variable

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score 346 · Answer 10 · 2026-03-29 15:51:39

346

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score 290 · Answer 11 · 2014-09-24 16:42:57

290

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score 766 · Answer 12 · 2026-03-29 22:14:32

766

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Conditional expectation of Brownian motion given its absolute value.

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score 328 · Answer 13 · 2026-03-29 20:11:30

328

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For $X_n$ iid, $S_n=\sum X_j$, $\mathscr{G}_n=\sigma(S_n,S_{n+1}, \dots)$, show $E(X_j \mid \mathscr{G}_n)=E(X_1 \mid S_n)$

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score 88 · Answer 14 · 2026-03-29 20:10:54

88

Views

Why this is a martingale?

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score 710 · Answer 15 · 2014-10-02 07:26:51

710

Views

Conditional Probability Problem for a Joint Distribution

Published on 02 Oct 2014 - 7:26

List Question

Show that $E[X \mid \sigma (\mathscr{G},\mathscr{H})] = E[X \mid \mathscr{G}]$ if $\mathscr{H}$ independent of $\sigma (\sigma (X),\mathscr{G})$

Expectation of a Random Variable multiplied by a Conditonal Expectation.

Computing the expectation of conditional variance in 2 ways

Old Notation for Conditional Expectation

Law of total probability in continous case

Expectation of a function of pairs of random variables

Exchangeability of random variables and conditional expectation

Definition and derivation of conditional expectation/probability

conditional expected value - Poisson process plus random variable

Prove variance inequality given conditional expectation

Marginalization question $\Pr[a] = E_X[\Pr[\ a|X\ ]\ ]$

Conditional expectation of Brownian motion given its absolute value.

For $X_n$ iid, $S_n=\sum X_j$, $\mathscr{G}_n=\sigma(S_n,S_{n+1}, \dots)$, show $E(X_j \mid \mathscr{G}_n)=E(X_1 \mid S_n)$

Why this is a martingale?

Conditional Probability Problem for a Joint Distribution

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