Question

Suppose $X_1, \dots, X_n, Y$ are independent random variables. Prove that $X = (X_1, \dots, X_n)$ and $Y$ are independent variables.

score 329 · Answer 1 · 2019-05-18 20:27:03

329

Views

Suppose $X_1, \dots, X_n, Y$ are independent random variables. Prove that $X = (X_1, \dots, X_n)$ and $Y$ are independent variables.

Published on 18 May 2019 - 20:27

score 207 · Answer 2 · 2019-05-18 21:21:43

207

Views

Applying the definition of mutual independence to outcomes of random variables

Published on 18 May 2019 - 21:21

score 39 · Answer 3 · 2019-05-19 20:54:21

39

Views

For a sequence of experiments where each $X$ is the number of trials until success with varying $p$, is each $X$ independent?

Published on 19 May 2019 - 20:54

score 61 · Answer 4 · 2019-05-20 12:05:08

61

Views

the independence property of conditional expectation

Published on 20 May 2019 - 12:05

score 40 · Answer 5 · 2019-05-21 10:59:30

40

Views

Help me elucidate what "the vectors $(B(d):d \in \mathcal {D_n })$ and $(Z_t:t \in \mathcal {D-D_n})$ are independent" mean.

Published on 21 May 2019 - 10:59

score 139 · Answer 6 · 2019-05-21 13:48:05

139

Views

How can I prove that these events are independent?

Published on 21 May 2019 - 13:48

score 61 · Answer 7 · 2026-03-26 03:18:50

61

Views

Moment generating function of two variables

Published on 26 Mar 2026 - 3:18

score 71 · Answer 8 · 2019-05-22 18:36:03

71

Views

Will these two random variables be independent?

Published on 22 May 2019 - 18:36

score 58 · Answer 9 · 2019-05-23 19:24:13

58

Views

Prove that $X_t = 1/c B_{c^2 t}$ with $c \gt 0$ is a Brownian Motion

Published on 23 May 2019 - 19:24

score 41 · Answer 10 · 2019-05-23 21:17:42

41

Views

Establishing independence between seemingly complementary random sums

Published on 23 May 2019 - 21:17

score 40 · Answer 11 · 2019-05-27 16:12:01

40

Views

Bounds for the number of independent variables on a finite probability space

Published on 27 May 2019 - 16:12

score 37 · Answer 12 · 2026-03-26 19:00:54

37

Views

Switching from $\sum\limits_{y \in E}\sum\limits_{n \geq 0}$ to $\sum\limits_{n \geq 0}\sum\limits_{y \in E}$

Published on 26 Mar 2026 - 19:00

score 43 · Answer 13 · 2019-06-01 07:40:52

43

Views

What is independence of events (in case of tossing an unbiased coin 3 times)?

Published on 01 Jun 2019 - 7:40

score 219 · Answer 14 · 2026-03-26 21:35:00

219

Views

Independence of random variables: sufficient conditions

Published on 26 Mar 2026 - 21:35

score 770 · Answer 15 · 2019-06-05 10:38:01

770

Views

Events are independent or not independent in the following example?

Published on 05 Jun 2019 - 10:38

List Question

Suppose $X_1, \dots, X_n, Y$ are independent random variables. Prove that $X = (X_1, \dots, X_n)$ and $Y$ are independent variables.

Applying the definition of mutual independence to outcomes of random variables

For a sequence of experiments where each $X$ is the number of trials until success with varying $p$, is each $X$ independent?

the independence property of conditional expectation

Help me elucidate what "the vectors $(B(d):d \in \mathcal {D_n })$ and $(Z_t:t \in \mathcal {D-D_n})$ are independent" mean.

How can I prove that these events are independent?

Moment generating function of two variables

Will these two random variables be independent?

Prove that $X_t = 1/c B_{c^2 t}$ with $c \gt 0$ is a Brownian Motion

Establishing independence between seemingly complementary random sums

Bounds for the number of independent variables on a finite probability space

Switching from $\sum\limits_{y \in E}\sum\limits_{n \geq 0}$ to $\sum\limits_{n \geq 0}\sum\limits_{y \in E}$

What is independence of events (in case of tossing an unbiased coin 3 times)?

Independence of random variables: sufficient conditions

Events are independent or not independent in the following example?

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