List questions from conditional-expectation

Published on 27 Mar 2026 - 14:58

132

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What is the expected number of rolls of a 6-sided die before getting a 2 followed immediately by a 3?

Published on 20 Apr 2020 - 17:35

400

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Expectation of a random variable conditioned on multiple events

Published on 20 Apr 2020 - 19:44

59

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How to find conditional expectation?

Published on 21 Apr 2020 - 11:01

214

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Conditional expectation $E(\xi^2\mid\xi\eta)$ where $\xi, \eta$ iid $N(0,1)$

Published on 21 Apr 2020 - 12:10

87

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Is this true: $\operatorname{Cov}(X,Y)=\operatorname{Cov}(E[X|Y],Y)$? Covariance of variables versus conditional expectations?

Published on 30 Mar 2026 - 16:46

97

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Showing that we can always decompose $Y = \mathbb{E}\left[Y|X\right] + \epsilon$.

Published on 27 Mar 2026 - 0:57

114

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Optimal worst case strategy for card game - double if red, half if black

Published on 25 Mar 2026 - 19:04

61

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Show that $E(X\mid Y)=E(X\mid A_1)1_{A_1}+\cdots +E(X\mid A_n)1_{A_n}$ when $\sigma(Y)=\sigma(\{A_1,\cdots A_n\})$

Published on 24 Apr 2020 - 12:37

69

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Why is $E[XY, X = i] = iE[Y, X = i]$?

Published on 29 Mar 2026 - 22:28

305

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About the William's Tower Property

Published on 25 Apr 2020 - 2:57

93

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Example for $E[E(X\mid\mathcal{G_1})\mid\mathcal{G_2}] \ne E[E(X\mid\mathcal{G_2})\mid\mathcal{G_1}]$

Published on 25 Apr 2020 - 7:44

68

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Conditional expectation under indepentent RV

Published on 25 Apr 2020 - 14:29

140

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Conditional Expectation of X conditioned on sigma algebra generated by X and Y where X,Y are independent

Published on 25 Apr 2020 - 18:54

36

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Why is Y|X the minimum

Published on 25 Apr 2020 - 22:35

List Question

Construction of a MGF for conditional random variables

What is the expected number of rolls of a 6-sided die before getting a 2 followed immediately by a 3?

Expectation of a random variable conditioned on multiple events

How to find conditional expectation?

Conditional expectation $E(\xi^2\mid\xi\eta)$ where $\xi, \eta$ iid $N(0,1)$

Is this true: $\operatorname{Cov}(X,Y)=\operatorname{Cov}(E[X|Y],Y)$? Covariance of variables versus conditional expectations?

Showing that we can always decompose $Y = \mathbb{E}\left[Y|X\right] + \epsilon$.

Optimal worst case strategy for card game - double if red, half if black

Show that $E(X\mid Y)=E(X\mid A_1)1_{A_1}+\cdots +E(X\mid A_n)1_{A_n}$ when $\sigma(Y)=\sigma(\{A_1,\cdots A_n\})$

Why is $E[XY, X = i] = iE[Y, X = i]$?

About the William's Tower Property

Example for $E[E(X\mid\mathcal{G_1})\mid\mathcal{G_2}] \ne E[E(X\mid\mathcal{G_2})\mid\mathcal{G_1}]$

Conditional expectation under indepentent RV

Conditional Expectation of X conditioned on sigma algebra generated by X and Y where X,Y are independent

Why is Y|X the minimum

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