Question

Counterexample for a statement about independence of random variables

score 287 · Answer 1 · 2026-04-14 23:33:42

287

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Counterexample for a statement about independence of random variables

Published on 14 Apr 2026 - 23:33

score 76 · Answer 2 · 2026-04-16 02:35:08

76

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If $X$ and $Y$ are both independent from $\mathscr {F}$, is $f(X,Y)$ also independent from $\mathscr{F}$?

Published on 16 Apr 2026 - 2:35

score 113 · Answer 3 · 2026-04-15 04:03:01

113

Views

Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$

Published on 15 Apr 2026 - 4:03

score 89 · Answer 4 · 2026-04-17 10:30:13

89

Views

Show that $Y_1=\frac{X_{(1)}}{X_{(2)}},Y_2=\frac{X_{(2)}}{X_{(3)}},\dots, Y_{n-1}=\frac{X_{(n-1)}}{X_{(n)}}$, and $Y_{(n)}=X_{(n)}$ are independent

Published on 17 Apr 2026 - 10:30

score 31 · Answer 5 · 2026-04-12 17:05:37

31

Views

Rewriting $P(X\geq f(Z) \wedge Z\leq z^*)$ using conditional dist. when $X, Z$ are independent

Published on 12 Apr 2026 - 17:05

score 161 · Answer 6 · 2026-04-12 14:41:06

161

Views

Showing conditional mutual independence

Published on 12 Apr 2026 - 14:41

score 31 · Answer 7 · 2026-04-15 10:49:59

31

Views

Non-existence of independent sets

Published on 15 Apr 2026 - 10:49

score 73 · Answer 8 · 2026-04-13 22:54:14

73

Views

Showing independence of a sequence of random variables

Published on 13 Apr 2026 - 22:54

score 146 · Answer 9 · 2026-04-08 18:58:53

146

Views

discrete random variables (vectors) and independence

Published on 08 Apr 2026 - 18:58

score 115 · Answer 10 · 2026-05-10 16:10:06

115

Views

Can $\limsup = \liminf$ only almost surely?

Published on 10 May 2026 - 16:10

score 370 · Answer 11 · 2026-04-16 19:26:08

370

Views

How can I compute an expression for $P(X_1>X_2>X_3>X_4)$ if $X_1,X_2,X_3,X_4$ are normal and mututally independent?

Published on 16 Apr 2026 - 19:26

score 162 · Answer 12 · 2026-04-14 10:44:28

162

Views

IID discrete but not a.s. equal

Published on 14 Apr 2026 - 10:44

score 75 · Answer 13 · 2026-03-28 09:09:06

75

Views

$\frac 1n \sum_{k=c+1}^n X_k X_{k-c}$ converges a.s to $0$ when $X_n$ is i.i.d. with mean $0$.

Published on 28 Mar 2026 - 9:09

score 100 · Answer 14 · 2026-05-05 09:55:54

100

Views

Independence of function of random variables

Published on 05 May 2026 - 9:55

score 1.4k · Answer 15 · 2026-05-10 17:00:42

1.4k

Views

Convergence of the random harmonic series $\sum_{n=1}^{\infty}\frac{X_{n}}{n}$

Published on 10 May 2026 - 17:00

List Question

Counterexample for a statement about independence of random variables

If $X$ and $Y$ are both independent from $\mathscr {F}$, is $f(X,Y)$ also independent from $\mathscr{F}$?

Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$

Show that $Y_1=\frac{X_{(1)}}{X_{(2)}},Y_2=\frac{X_{(2)}}{X_{(3)}},\dots, Y_{n-1}=\frac{X_{(n-1)}}{X_{(n)}}$, and $Y_{(n)}=X_{(n)}$ are independent

Rewriting $P(X\geq f(Z) \wedge Z\leq z^*)$ using conditional dist. when $X, Z$ are independent

Showing conditional mutual independence

Non-existence of independent sets

Showing independence of a sequence of random variables

discrete random variables (vectors) and independence

Can $\limsup = \liminf$ only almost surely?

How can I compute an expression for $P(X_1>X_2>X_3>X_4)$ if $X_1,X_2,X_3,X_4$ are normal and mututally independent?

IID discrete but not a.s. equal

$\frac 1n \sum_{k=c+1}^n X_k X_{k-c}$ converges a.s to $0$ when $X_n$ is i.i.d. with mean $0$.

Independence of function of random variables

Convergence of the random harmonic series $\sum_{n=1}^{\infty}\frac{X_{n}}{n}$

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