List questions from conditional-expectation

Published on 14 Apr 2026 - 7:43

110

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How to calculate conditional expectation $\mathbb{E}[g(x)\ | \ x\geq Q]$ for $x\sim \exp(1)$

Published on 15 Apr 2026 - 19:32

40

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Expression of conditional expectation using integrals, similar to expression when conditioning on an event rather than a random variable

Published on 14 Apr 2026 - 1:19

80

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Proving supermartingale (sequence of uniformly distributed random variables)

Published on 16 Apr 2026 - 4:52

141

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Finding the conditional expectation of a max/min random variable

Published on 10 Apr 2026 - 3:27

35

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Show that this function is a conditional probability

Published on 11 Apr 2026 - 21:52

126

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Probability inequalities with indicator variables

Published on 14 Apr 2026 - 16:07

39

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Probability of $w<X$ where $X$ is a random variable equals the expectation of the probability of $w<X$ where $X$ is a constant

Published on 13 Apr 2026 - 13:11

57

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Question on tower property

Published on 12 Apr 2026 - 15:08

84

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Coins in two piles game — where have I gone wrong?

Published on 14 Apr 2026 - 17:16

95

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Let $\mathcal{G}$ be a $\sigma$-algebra. Show that if $\mathbb{E}((\mathbb{E}(X|\mathcal{G}))^2)=\mathbb{E}(X^2)$ then $\mathbb{E}(X|\mathcal{G})=X$?

Published on 15 Apr 2026 - 18:21

141

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Understanding the construction of the smallest filtration making a random time a stopping time from Protter

Published on 17 Apr 2026 - 7:06

52

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On conditional expectation

Published on 13 Apr 2026 - 23:01

54

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$X$ is $\mathscr{G} (\subset \mathscr{F})$ measurable if $E[XH]=0$ for all bounded $H$ such that $E[H|\mathscr{G}]=0$.

Published on 13 Apr 2026 - 6:53

65

Views

The meaning of E[X|Y] = E[X]

Published on 14 Apr 2026 - 18:13

List Question

An upper bound on Conditional Variance

How to calculate conditional expectation $\mathbb{E}[g(x)\ | \ x\geq Q]$ for $x\sim \exp(1)$

Expression of conditional expectation using integrals, similar to expression when conditioning on an event rather than a random variable

Proving supermartingale (sequence of uniformly distributed random variables)

Finding the conditional expectation of a max/min random variable

Show that this function is a conditional probability

Probability inequalities with indicator variables

Probability of $w<X$ where $X$ is a random variable equals the expectation of the probability of $w<X$ where $X$ is a constant

Question on tower property

Coins in two piles game — where have I gone wrong?

Let $\mathcal{G}$ be a $\sigma$-algebra. Show that if $\mathbb{E}((\mathbb{E}(X|\mathcal{G}))^2)=\mathbb{E}(X^2)$ then $\mathbb{E}(X|\mathcal{G})=X$?

Understanding the construction of the smallest filtration making a random time a stopping time from Protter

On conditional expectation

$X$ is $\mathscr{G} (\subset \mathscr{F})$ measurable if $E[XH]=0$ for all bounded $H$ such that $E[H|\mathscr{G}]=0$.

The meaning of E[X|Y] = E[X]

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