Question

Showing $\mathbb{E}[\exp(\lambda X) | G] \leq \exp\left(\frac{\lambda^{2}}{2}\right)$ for a random variable $X$ and sub-sigma-algebra $\mathcal G$

score 138 · Answer 1 · 2026-04-14 17:02:13

138

Views

Showing $\mathbb{E}[\exp(\lambda X) | G] \leq \exp\left(\frac{\lambda^{2}}{2}\right)$ for a random variable $X$ and sub-sigma-algebra $\mathcal G$

Published on 14 Apr 2026 - 17:02

score 43 · Answer 2 · 2026-04-16 02:31:49

43

Views

Find an expression for $X_n = E[Y | \mathcal{F}_n]$ with $\mathcal{F}_n = \sigma(\{1\}, \{2\}, \ldots, \{n-1\}, \{n, n+1, \ldots\})$

Published on 16 Apr 2026 - 2:31

score 50 · Answer 3 · 2026-04-10 11:38:52

50

Views

Learning Conditional expectation: Understanding a simple example

Published on 10 Apr 2026 - 11:38

score 50 · Answer 4 · 2026-04-12 12:37:22

50

Views

Explicit formula to $\mathbb{E}[Y|X_1,..,X_n]$?

Published on 12 Apr 2026 - 12:37

score 58 · Answer 5 · 2026-04-10 18:44:49

58

Views

Conditional expectations as functions

Published on 10 Apr 2026 - 18:44

score 76 · Answer 6 · 2026-04-16 04:12:05

76

Views

how to compute E[X] given X+Y>1, X, Y iid ~ uniform (0, 1)

Published on 16 Apr 2026 - 4:12

score 165 · Answer 7 · 2026-04-16 06:34:28

165

Views

Why is the expected number of draws given $k$ coupons so similar to the expected number of draws required to obtain $k$ coupons?

Published on 16 Apr 2026 - 6:34

score 170 · Answer 8 · 2026-04-17 08:41:13

170

Views

If $Y, X, Z$ are random variables, is it true that $E[Y|X=x] = \sum_{z} E[Y|X=x, Z=z]P(Z=z|X=x)$ by law of total expectation?

Published on 17 Apr 2026 - 8:41

score 39 · Answer 9 · 2026-04-12 18:03:00

39

Views

Computing conditional expectation with respect to random variable

Published on 12 Apr 2026 - 18:03

score 37 · Answer 10 · 2026-04-14 04:32:17

37

Views

Expected value of trials for "two in a row"

Published on 14 Apr 2026 - 4:32

score 83 · Answer 11 · 2026-03-26 04:14:12

83

Views

A new convergence problem for the conditional expectation

Published on 26 Mar 2026 - 4:14

score 128 · Answer 12 · 2026-04-15 11:55:14

128

Views

Variance of a conditional expectation and conditional variance

Published on 15 Apr 2026 - 11:55

score 64 · Answer 13 · 2026-04-10 19:45:45

64

Views

How to find the $E(X|\mathcal{G})$?

Published on 10 Apr 2026 - 19:45

score 44 · Answer 14 · 2026-04-17 09:56:35

44

Views

Find Conditional expectation of uniform variables ...

Published on 17 Apr 2026 - 9:56

score 60 · Answer 15 · 2026-04-10 20:15:52

60

Views

Integrating density over measurable sets yields probability?

Published on 10 Apr 2026 - 20:15

List Question

Showing $\mathbb{E}[\exp(\lambda X) | G] \leq \exp\left(\frac{\lambda^{2}}{2}\right)$ for a random variable $X$ and sub-sigma-algebra $\mathcal G$

Find an expression for $X_n = E[Y | \mathcal{F}_n]$ with $\mathcal{F}_n = \sigma(\{1\}, \{2\}, \ldots, \{n-1\}, \{n, n+1, \ldots\})$

Learning Conditional expectation: Understanding a simple example

Explicit formula to $\mathbb{E}[Y|X_1,..,X_n]$?

Conditional expectations as functions

how to compute E[X] given X+Y>1, X, Y iid ~ uniform (0, 1)

Why is the expected number of draws given $k$ coupons so similar to the expected number of draws required to obtain $k$ coupons?

If $Y, X, Z$ are random variables, is it true that $E[Y|X=x] = \sum_{z} E[Y|X=x, Z=z]P(Z=z|X=x)$ by law of total expectation?

Computing conditional expectation with respect to random variable

Expected value of trials for "two in a row"

A new convergence problem for the conditional expectation

Variance of a conditional expectation and conditional variance

How to find the $E(X|\mathcal{G})$?

Find Conditional expectation of uniform variables ...

Integrating density over measurable sets yields probability?

Trending Questions

Popular # Hahtags

Popular Questions