Question

The existence and uniqueness of conditional expectation of a positive infinite mean random variable --- Durrett 4.1.3

score 408 · Answer 1 · 2019-11-16 16:48:22

408

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The existence and uniqueness of conditional expectation of a positive infinite mean random variable --- Durrett 4.1.3

Published on 16 Nov 2019 - 16:48

score 73 · Answer 2 · 2019-11-17 10:31:25

73

Views

Equality of conditional expectations for random vectors

Published on 17 Nov 2019 - 10:31

score 87 · Answer 3 · 2019-11-17 14:56:51

87

Views

Show that : $ \lim_{n} \mathbb{E}[X_n\mid \mathcal{B}]= \mathbb{E}[X\mid \mathcal{B}]$ in $L^{p} $

Published on 17 Nov 2019 - 14:56

score 530 · Answer 4 · 2019-11-17 16:22:44

530

Views

Clarification of definitions of function being a contraction in $L_{p}$ space

Published on 17 Nov 2019 - 16:22

score 223 · Answer 5 · 2026-03-28 02:07:59

223

Views

Evaluate conditional expectation of $X^2$ given $\sin(X)$ and uniform distribution of $X$ over $[0,\pi]$

Published on 28 Mar 2026 - 2:07

score 255 · Answer 6 · 2019-11-17 17:48:48

255

Views

Explicitly compute conditional expectation of a random variable on the discrete probability space

Published on 17 Nov 2019 - 17:48

score 87 · Answer 7 · 2019-11-17 21:15:31

87

Views

Show that : $ \mathbb{P}[\max_{i=1}^{n}{X_i}\ge \epsilon]\leq\frac {1}{\epsilon}\int_{[\max_{i=1}^{n}{X_i}\ge \epsilon]} X_n d\mathbb{P} $

Published on 17 Nov 2019 - 21:15

score 170 · Answer 8 · 2019-11-17 21:40:04

170

Views

From table of discrete joint distribution of $X$ and $Y$ to read the distribution of $X$ and $Y$ and $\mathbb{E}(Y|X)$ --- Durrett 1.4.2

Published on 17 Nov 2019 - 21:40

score 101 · Answer 9 · 2026-03-25 14:21:03

101

Views

Durrett Theorem 4.1.8: minimizes the mean square error $\mathbb{E}(X-Y)^{2}$ using conditional expectation $\mathbb{E}(X|\mathcal{F})$

Published on 25 Mar 2026 - 14:21

score 82 · Answer 10 · 2026-03-28 04:53:14

82

Views

Kalman filter: Bayesian derivation, can $E(X_t\mid \{y\}_1^t)=arg\,\underset{x_t}{max}\;P(X_t=x_t\mid \{y\}_1^t)$?

Published on 28 Mar 2026 - 4:53

score 49 · Answer 11 · 2019-11-18 11:58:51

49

Views

$\mathbb{E}[X_{n}\mid \mathcal{F}_n]$ does not converge in probability to $0$.

Published on 18 Nov 2019 - 11:58

score 31 · Answer 12 · 2019-11-20 14:03:19

31

Views

What conditions must $X$ fulfill for conditional expectation $\mathbb {E} [X|\mathcal{B} ]$ to exist?

Published on 20 Nov 2019 - 14:03

score 389 · Answer 13 · 2026-03-27 00:02:06

389

Views

Conditional Expectation of a Poisson Variable on an Exponential Variable

Published on 27 Mar 2026 - 0:02

score 195 · Answer 14 · 2019-11-21 11:56:00

195

Views

Joint Distribution and Regular Conditional Probability Distribution ---Durrett 4.1.12

Published on 21 Nov 2019 - 11:56

score 244 · Answer 15 · 2019-11-21 17:39:01

244

Views

Inequality with conditional expectation of positive random variables

Published on 21 Nov 2019 - 17:39

List Question

The existence and uniqueness of conditional expectation of a positive infinite mean random variable --- Durrett 4.1.3

Equality of conditional expectations for random vectors

Show that : $ \lim_{n} \mathbb{E}[X_n\mid \mathcal{B}]= \mathbb{E}[X\mid \mathcal{B}]$ in $L^{p} $

Clarification of definitions of function being a contraction in $L_{p}$ space

Evaluate conditional expectation of $X^2$ given $\sin(X)$ and uniform distribution of $X$ over $[0,\pi]$

Explicitly compute conditional expectation of a random variable on the discrete probability space

Show that : $ \mathbb{P}[\max_{i=1}^{n}{X_i}\ge \epsilon]\leq\frac {1}{\epsilon}\int_{[\max_{i=1}^{n}{X_i}\ge \epsilon]} X_n d\mathbb{P} $

From table of discrete joint distribution of $X$ and $Y$ to read the distribution of $X$ and $Y$ and $\mathbb{E}(Y|X)$ --- Durrett 1.4.2

Durrett Theorem 4.1.8: minimizes the mean square error $\mathbb{E}(X-Y)^{2}$ using conditional expectation $\mathbb{E}(X|\mathcal{F})$

Kalman filter: Bayesian derivation, can $E(X_t\mid \{y\}_1^t)=arg\,\underset{x_t}{max}\;P(X_t=x_t\mid \{y\}_1^t)$?

$\mathbb{E}[X_{n}\mid \mathcal{F}_n]$ does not converge in probability to $0$.

What conditions must $X$ fulfill for conditional expectation $\mathbb {E} [X|\mathcal{B} ]$ to exist?

Conditional Expectation of a Poisson Variable on an Exponential Variable

Joint Distribution and Regular Conditional Probability Distribution ---Durrett 4.1.12

Inequality with conditional expectation of positive random variables

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