Question

If $E[Y|X]=X$ and $Z$ independent of $(X,Y)$, what is the conditional distribution of $E[Y|X,X+Y+Z]$ given $(X,Y)$?

score 106 · Answer 1 · 2026-04-15 12:42:27

106

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If $E[Y|X]=X$ and $Z$ independent of $(X,Y)$, what is the conditional distribution of $E[Y|X,X+Y+Z]$ given $(X,Y)$?

Published on 15 Apr 2026 - 12:42

score 113 · Answer 2 · 2026-04-09 15:57:31

113

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An Intuitive Definition for Independence of Events

Published on 09 Apr 2026 - 15:57

score 54 · Answer 3 · 2026-04-13 03:51:05

54

Views

How to calculate the overall probability of an event occurring, if the probability is increased after a certain number of trials.

Published on 13 Apr 2026 - 3:51

score 24 · Answer 4 · 2026-05-14 10:07:26

24

Views

Confusion on proving the independence of two events

Published on 14 May 2026 - 10:07

score 72 · Answer 5 · 2026-04-13 04:12:18

72

Views

Question about KL divergence and this formula.

Published on 13 Apr 2026 - 4:12

score 185 · Answer 6 · 2026-04-13 03:32:30

185

Views

Conditional expectation and an independent $\sigma$-algebra

Published on 13 Apr 2026 - 3:32

score 57 · Answer 7 · 2026-04-14 05:47:17

57

Views

Why do I have $\Bbb{E}\left(|\Bbb{E}(X|Y)|\right)=\sum_{y\in E'} \Bbb{E}\left(|\Bbb{E}(X|Y)|\Bbb{1}_{Y=y}\right)$?

Published on 14 Apr 2026 - 5:47

score 57 · Answer 8 · 2026-04-13 18:45:58

57

Views

You have a fair coin and a biased coin. What is the probability the second flip will be heads if the first flip was?

Published on 13 Apr 2026 - 18:45

score 52 · Answer 9 · 2026-04-13 20:31:51

52

Views

How can I show that $P(S_n \ge 0 \mid T_0 = k) = 1/2?$ I understand it intuitively, but I get lost with notation.

Published on 13 Apr 2026 - 20:31

score 74 · Answer 10 · 2026-04-14 18:11:32

74

Views

Considering that the two selected balls are white, what is the probability that urn III was chosen?

Published on 14 Apr 2026 - 18:11

score 39 · Answer 11 · 2026-04-10 17:21:06

39

Views

Understanding a simplification of a conditional expectation

Published on 10 Apr 2026 - 17:21

score 43 · Answer 12 · 2026-04-11 18:04:34

43

Views

Looking for help calculating expectation of a “modified” geometric distribution - 3 bit signals

Published on 11 Apr 2026 - 18:04

score 71 · Answer 13 · 2026-04-14 10:40:37

71

Views

Sum of random number of independent random variables (with dependency)

Published on 14 Apr 2026 - 10:40

score 186 · Answer 14 · 2026-04-10 19:53:40

186

Views

Distribution of randomly truncated random variable

Published on 10 Apr 2026 - 19:53

score 49 · Answer 15 · 2026-04-16 00:32:03

49

Views

Find $P(X\ge1|X\le6)$ from the cdf

Published on 16 Apr 2026 - 0:32

List Question

If $E[Y|X]=X$ and $Z$ independent of $(X,Y)$, what is the conditional distribution of $E[Y|X,X+Y+Z]$ given $(X,Y)$?

An Intuitive Definition for Independence of Events

How to calculate the overall probability of an event occurring, if the probability is increased after a certain number of trials.

Confusion on proving the independence of two events

Question about KL divergence and this formula.

Conditional expectation and an independent $\sigma$-algebra

Why do I have $\Bbb{E}\left(|\Bbb{E}(X|Y)|\right)=\sum_{y\in E'} \Bbb{E}\left(|\Bbb{E}(X|Y)|\Bbb{1}_{Y=y}\right)$?

You have a fair coin and a biased coin. What is the probability the second flip will be heads if the first flip was?

How can I show that $P(S_n \ge 0 \mid T_0 = k) = 1/2?$ I understand it intuitively, but I get lost with notation.

Considering that the two selected balls are white, what is the probability that urn III was chosen?

Understanding a simplification of a conditional expectation

Looking for help calculating expectation of a “modified” geometric distribution - 3 bit signals

Sum of random number of independent random variables (with dependency)

Distribution of randomly truncated random variable

Find $P(X\ge1|X\le6)$ from the cdf

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