List questions from conditional-expectation

Published on 09 Apr 2026 - 18:36

37

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$\mathbb{E}[\mathbb{1}_{\{Y\in B\}}|X]=Q(X,B)$ where $Q(x,B):=\sum\limits_{y\in B}\mathbb{P}(Y=y\mid X=x)$?

Published on 15 Apr 2026 - 21:34

48

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Variance of $x + \xi(x)$, where $\xi(x) \sim \operatorname{Bin}(x, p)$.

Published on 15 Apr 2026 - 18:11

172

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Show that $E[f(X_1,X_2)\mid \mathcal{F}_n]=\frac{2}{n(n-1)}\sum_{ 1 \leq p<q \leq n}f(X_p,X_q)$

Published on 17 Apr 2026 - 13:54

83

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Why does the probability of the sum of two independent random variables equals the conditional expectation

Published on 13 Apr 2026 - 7:31

581

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Expectation of the product of random variables

Published on 13 Apr 2026 - 2:17

126

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Conditional Expectation of Function of I.I.D Random Variables

Published on 14 Apr 2026 - 8:14

157

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If for every $x>0,P(|X_k|>x) \leq P(Y>x)$ then $\lim_k E[X_k|\mathcal{G}]=E[X|\mathcal{G}]$ a.s.?

Published on 16 Apr 2026 - 23:55

85

Views

How to calculate conditional expectation of two independent poison r.v. ($E(N_1|N_1+N_2)$)

Published on 12 Apr 2026 - 19:55

106

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How can I integrate $\int_{x}^{\infty}\lambda ye^{-\lambda(y-x)}\mathrm{d}y$ by parts

Published on 14 Apr 2026 - 16:35

48

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How to compare two expectation

Published on 10 Apr 2026 - 3:00

51

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How to find the conditional probability density function $f_{X|X\geq 0}$ where $X\sim N(\mu , {\sigma}^2)$?

Published on 15 Apr 2026 - 3:46

42

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Conditional Expectation of Random Functional

Published on 11 Apr 2026 - 10:13

127

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What is the exact relationship between $E(Y\mid X=x)$ and $E(Y\mid X)$?

Published on 13 Apr 2026 - 22:36

295

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Proving conditional expectation is bounded if expectation is bounded

Published on 11 Apr 2026 - 23:08

List Question

Expected value of a function, is this true? why?

$\mathbb{E}[\mathbb{1}_{\{Y\in B\}}|X]=Q(X,B)$ where $Q(x,B):=\sum\limits_{y\in B}\mathbb{P}(Y=y\mid X=x)$?

Variance of $x + \xi(x)$, where $\xi(x) \sim \operatorname{Bin}(x, p)$.

Show that $E[f(X_1,X_2)\mid \mathcal{F}_n]=\frac{2}{n(n-1)}\sum_{ 1 \leq p<q \leq n}f(X_p,X_q)$

Why does the probability of the sum of two independent random variables equals the conditional expectation

Expectation of the product of random variables

Conditional Expectation of Function of I.I.D Random Variables

If for every $x>0,P(|X_k|>x) \leq P(Y>x)$ then $\lim_k E[X_k|\mathcal{G}]=E[X|\mathcal{G}]$ a.s.?

How to calculate conditional expectation of two independent poison r.v. ($E(N_1|N_1+N_2)$)

How can I integrate $\int_{x}^{\infty}\lambda ye^{-\lambda(y-x)}\mathrm{d}y$ by parts

How to compare two expectation

How to find the conditional probability density function $f_{X|X\geq 0}$ where $X\sim N(\mu , {\sigma}^2)$?

Conditional Expectation of Random Functional

What is the exact relationship between $E(Y\mid X=x)$ and $E(Y\mid X)$?

Proving conditional expectation is bounded if expectation is bounded

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