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Product of Independent Random Variables - Conditional Expectation

score 690 · Answer 1 · 2016-02-25 15:54:51

690

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Product of Independent Random Variables - Conditional Expectation

Published on 25 Feb 2016 - 15:54

score 113 · Answer 2 · 2016-02-26 23:52:43

113

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My law schools shady response to mathematical improbability.

Published on 26 Feb 2016 - 23:52

score 1.6k · Answer 3 · 2026-04-03 05:14:33

1.6k

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Let $X$ be a standard normal random variable and $Y = X^2$.

Published on 03 Apr 2026 - 5:14

score 118 · Answer 4 · 2016-03-01 11:43:18

118

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If $f_n \to g$ in $L_2$, and that $f_n = \mathbb{E}(f \mid \mathcal{F}_n)$, show if $f$ continuous, then $g(x)=f(x)$ for all $x$ with probability 1?

Published on 01 Mar 2016 - 11:43

score 227 · Answer 5 · 2016-03-02 16:20:23

227

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Estimator for conditional expectation w.r.t an event

Published on 02 Mar 2016 - 16:20

score 45 · Answer 6 · 2026-03-30 15:36:43

45

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Determining whether or not random variables are correlated

Published on 30 Mar 2026 - 15:36

score 40 · Answer 7 · 2016-03-05 06:12:28

40

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Is $\max\{E(X|Y_1),\cdots, E(X|Y_n)\}=E(X|Y_1,\cdots, Y_n)$

Published on 05 Mar 2016 - 6:12

score 2.6k · Answer 8 · 2026-04-01 15:12:19

2.6k

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How to show that $E[E[X\mid Y]\mid Y] = E[X\mid Y]$

Published on 01 Apr 2026 - 15:12

score 302 · Answer 9 · 2016-03-08 16:08:21

302

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Consider a probability space $\Omega$ with four elements $a,b,c,d$. Define $\sigma$-algebra $F$ on $\Omega$-collection of subsets of $\Omega$.

Published on 08 Mar 2016 - 16:08

score 492 · Answer 10 · 2016-03-09 06:57:17

492

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Conditional Holder inequality with $p=1,\infty$.

Published on 09 Mar 2016 - 6:57

score 98 · Answer 11 · 2026-04-02 23:41:25

98

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If $Y_1, \ldots, Y_n \sim Poisson(\lambda)$ are iid, how to show that $E(Y_1 | T = \sum_{i=1}^{n}Y_i) = \frac{T}{n}$?

Published on 02 Apr 2026 - 23:41

score 51 · Answer 12 · 2016-03-10 01:53:51

51

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Let $X$ and $Y$ be random variables with a discrete joint distribution, and let $Z = r(x, y)$ for some function $r$.

Published on 10 Mar 2016 - 1:53

score 125 · Answer 13 · 2016-03-10 22:46:13

125

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Conditional expectation on different probability measure

Published on 10 Mar 2016 - 22:46

score 267 · Answer 14 · 2026-03-30 05:10:17

267

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Conditional Expectation.

Published on 30 Mar 2026 - 5:10

score 168 · Answer 15 · 2026-04-06 08:44:54

168

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If $(M_t)_{t \in [a,b]}$ is a martingale, then $t \mapsto E [ M_t ]$ is continuous.

Published on 06 Apr 2026 - 8:44

List Question

Product of Independent Random Variables - Conditional Expectation

My law schools shady response to mathematical improbability.

Let $X$ be a standard normal random variable and $Y = X^2$.

If $f_n \to g$ in $L_2$, and that $f_n = \mathbb{E}(f \mid \mathcal{F}_n)$, show if $f$ continuous, then $g(x)=f(x)$ for all $x$ with probability 1?

Estimator for conditional expectation w.r.t an event

Determining whether or not random variables are correlated

Is $\max\{E(X|Y_1),\cdots, E(X|Y_n)\}=E(X|Y_1,\cdots, Y_n)$

How to show that $E[E[X\mid Y]\mid Y] = E[X\mid Y]$

Consider a probability space $\Omega$ with four elements $a,b,c,d$. Define $\sigma$-algebra $F$ on $\Omega$-collection of subsets of $\Omega$.

Conditional Holder inequality with $p=1,\infty$.

If $Y_1, \ldots, Y_n \sim Poisson(\lambda)$ are iid, how to show that $E(Y_1 | T = \sum_{i=1}^{n}Y_i) = \frac{T}{n}$?

Let $X$ and $Y$ be random variables with a discrete joint distribution, and let $Z = r(x, y)$ for some function $r$.

Conditional expectation on different probability measure

Conditional Expectation.

If $(M_t)_{t \in [a,b]}$ is a martingale, then $t \mapsto E [ M_t ]$ is continuous.

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