Question

Expectation of CIR process Conditional on OU process

score 164 · Answer 1 · 2026-04-09 10:53:11

164

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Expectation of CIR process Conditional on OU process

Published on 09 Apr 2026 - 10:53

score 223 · Answer 2 · 2026-04-17 09:51:50

223

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Example $E[X|Y] = E[X]$ for $X, Y$ dependent

Published on 17 Apr 2026 - 9:51

score 166 · Answer 3 · 2026-04-17 13:42:10

166

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Detailed properties of conditional expectation

Published on 17 Apr 2026 - 13:42

score 230 · Answer 4 · 2026-04-14 12:41:38

230

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$X$ is a random variable with finite variance. Let $Y=\alpha X + \beta$. Compute $E[(Y-E[Y|X])^2]$.

Published on 14 Apr 2026 - 12:41

score 32 · Answer 5 · 2026-04-12 08:54:20

32

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$Y=AX + BX^3$. Compute Var(Y|X=x) $X$ has distribution $N(1,1)$ and $A$ & $B$ both have distribution $U(-1,1)$.

Published on 12 Apr 2026 - 8:54

score 22 · Answer 6 · 2026-04-14 14:19:35

22

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$A$ has distribution $U(-1,1)$. $Y = AX$. $X$ and $A$ are independent (and can assume $X^2$ and $A^2$ are independent). Compute $E[(Y-E[Y|X])^2].

Published on 14 Apr 2026 - 14:19

score 38 · Answer 7 · 2026-04-16 12:10:11

38

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Independence of $Y,Z$ where $Y|X = I(0<x<b)$ and $Z|X=I(a<x<1)$, for $0<a<b<1$

Published on 16 Apr 2026 - 12:10

score 93 · Answer 8 · 2026-04-09 06:50:08

93

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expected value for random number selection

Published on 09 Apr 2026 - 6:50

score 23 · Answer 9 · 2026-04-16 19:05:45

23

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Reference for $\operatorname E\left[f\circ X\mid X^{-1}(\mathcal F)\right]=\operatorname E_{\mathcal L(X)}\left[f\mid\mathcal F\right]\circ X$

Published on 16 Apr 2026 - 19:05

score 133 · Answer 10 · 2026-03-31 02:07:58

133

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Expectation of $|x^{2} - y^{2}|$ when $x$ and $y$ are bivariate normal

Published on 31 Mar 2026 - 2:07

score 300 · Answer 11 · 2026-04-12 18:46:33

300

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Trials in an event are performed until one gets k consecutive successes. $X_k$ Is the number of successes in all those trials. Find $E[X_k]$?

Published on 12 Apr 2026 - 18:46

score 141 · Answer 12 · 2026-04-15 01:23:20

141

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Calculate the conditional expectation of X given the order statistics?

Published on 15 Apr 2026 - 1:23

score 121 · Answer 13 · 2026-04-16 00:48:01

121

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Conditional expectation $E[f(X,Y)|\mathcal F]$ with $Y$ $\mathcal F$-measurable

Published on 16 Apr 2026 - 0:48

score 283 · Answer 14 · 2026-04-15 05:36:22

283

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Prove $X=Y$ from $E[X|Y]=Y$ and $E[Y|X]=X$

Published on 15 Apr 2026 - 5:36

score 67 · Answer 15 · 2026-04-15 15:06:52

67

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Suppose $X, Y, Z$ are random variables. How to write $E(X)$ as a function of $E(X|Y, Z)$?

Published on 15 Apr 2026 - 15:06

List Question

Expectation of CIR process Conditional on OU process

Example $E[X|Y] = E[X]$ for $X, Y$ dependent

Detailed properties of conditional expectation

$X$ is a random variable with finite variance. Let $Y=\alpha X + \beta$. Compute $E[(Y-E[Y|X])^2]$.

$Y=AX + BX^3$. Compute Var(Y|X=x) $X$ has distribution $N(1,1)$ and $A$ & $B$ both have distribution $U(-1,1)$.

$A$ has distribution $U(-1,1)$. $Y = AX$. $X$ and $A$ are independent (and can assume $X^2$ and $A^2$ are independent). Compute $E[(Y-E[Y|X])^2].

Independence of $Y,Z$ where $Y|X = I(0<x<b)$ and $Z|X=I(a<x<1)$, for $0<a<b<1$

expected value for random number selection

Reference for $\operatorname E\left[f\circ X\mid X^{-1}(\mathcal F)\right]=\operatorname E_{\mathcal L(X)}\left[f\mid\mathcal F\right]\circ X$

Expectation of $|x^{2} - y^{2}|$ when $x$ and $y$ are bivariate normal

Trials in an event are performed until one gets k consecutive successes. $X_k$ Is the number of successes in all those trials. Find $E[X_k]$?

Calculate the conditional expectation of X given the order statistics?

Conditional expectation $E[f(X,Y)|\mathcal F]$ with $Y$ $\mathcal F$-measurable

Prove $X=Y$ from $E[X|Y]=Y$ and $E[Y|X]=X$

Suppose $X, Y, Z$ are random variables. How to write $E(X)$ as a function of $E(X|Y, Z)$?

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