Question

Counterexample for a statement about independence of random variables

score 284 · Answer 1 · 2018-05-06 05:34:41

284

Views

Counterexample for a statement about independence of random variables

Published on 06 May 2018 - 5:34

score 73 · Answer 2 · 2018-05-06 15:29:38

73

Views

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

Published on 06 May 2018 - 15:29

score 111 · Answer 3 · 2026-03-25 09:29:50

111

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 25 Mar 2026 - 9:29

score 87 · Answer 4 · 2026-03-25 09:29:49

87

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 25 Mar 2026 - 9:29

score 28 · Answer 5 · 2018-05-10 02:58:18

28

Views

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

Published on 10 May 2018 - 2:58

score 158 · Answer 6 · 2018-05-10 14:07:49

158

Views

Showing conditional mutual independence

Published on 10 May 2018 - 14:07

score 28 · Answer 7 · 2018-05-10 23:23:25

28

Views

Non-existence of independent sets

Published on 10 May 2018 - 23:23

score 70 · Answer 8 · 2018-05-11 12:57:28

70

Views

Showing independence of a sequence of random variables

Published on 11 May 2018 - 12:57

score 143 · Answer 9 · 2018-05-11 17:04:36

143

Views

discrete random variables (vectors) and independence

Published on 11 May 2018 - 17:04

score 112 · Answer 10 · 2026-03-25 09:34:41

112

Views

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

Published on 25 Mar 2026 - 9:34

score 367 · Answer 11 · 2018-05-15 13:13:41

367

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 15 May 2018 - 13:13

score 159 · Answer 12 · 2018-05-15 15:07:18

159

Views

IID discrete but not a.s. equal

Published on 15 May 2018 - 15:07

score 73 · Answer 13 · 2026-03-25 01:40:03

73

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 25 Mar 2026 - 1:40

score 95 · Answer 14 · 2026-03-22 12:41:57

95

Views

Independence of function of random variables

Published on 22 Mar 2026 - 12:41

score 1.4k · Answer 15 · 2026-03-25 06:15:31

1.4k

Views

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

Published on 25 Mar 2026 - 6:15

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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