由买买提看人间百态

boards

本页内容为未名空间相应帖子的节选和存档,一周内的贴子最多显示50字,超过一周显示500字 访问原贴
Mathematics版 - 求助:一个有些难度的概率不等式
相关主题
Ask questions on Latin Hypercube sampling真心求教一道随机收敛的问题
矩阵乘积的特征值Re: 请教:这个不等式如何证明?
漫谈扭结(四)请教:这个不等式如何证明?[合集]
请教二元丢番图方程Re: is there a simple way to prove..?
关于Zernike polynomials请教一下Re: How to prove this equality?
Help please: is there any correlation between the two data set?Re: 一个不等式的证明
A ceiling function problemRe: 求一个不等式底解法,谢谢先.
matrix exponential question级数的估计
相关话题的讨论汇总
话题: 不等式话题: 有类话题: correlated话题: variables
进入Mathematics版参与讨论
1 (共1页)
z****j
发帖数: 131
1
There are 3 non-degenerated random variables Z,X,T, and
(1) Z,X independent, (2) both Z and X are correlated to T.
(3) T is positive.
How to prove
|E(Z*X*T)E(T)-E(Z*T)E(X*T)| <=
\sqrt{(E(Z^2*T)E(T)-E^2(Z*T))* (E(X^2*T)E(T)-E^2(X*T))}.
谁能证明一下?或者谁见过有类似的不等式的相关文献,我也可以去查询一下。
谢谢您的关注!
r*****r
发帖数: 630
2
First show if Y is a r.v. then
(E(YT))^2 -E(Y^2T)E(T) <=0;
then let Y=X+aZ, a is a real number,
consider LHS as a polynomial of a.
It seems I did not use (1) if every term makes sense in the inequality.

【在 z****j 的大作中提到】
: There are 3 non-degenerated random variables Z,X,T, and
: (1) Z,X independent, (2) both Z and X are correlated to T.
: (3) T is positive.
: How to prove
: |E(Z*X*T)E(T)-E(Z*T)E(X*T)| <=
: \sqrt{(E(Z^2*T)E(T)-E^2(Z*T))* (E(X^2*T)E(T)-E^2(X*T))}.
: 谁能证明一下?或者谁见过有类似的不等式的相关文献,我也可以去查询一下。
: 谢谢您的关注!

z****j
发帖数: 131
3
很好。谢谢大侠!

【在 r*****r 的大作中提到】
: First show if Y is a r.v. then
: (E(YT))^2 -E(Y^2T)E(T) <=0;
: then let Y=X+aZ, a is a real number,
: consider LHS as a polynomial of a.
: It seems I did not use (1) if every term makes sense in the inequality.

1 (共1页)
进入Mathematics版参与讨论
相关主题
级数的估计关于Zernike polynomials请教一下
Waring's formulaHelp please: is there any correlation between the two data set?
请教一个证明题A ceiling function problem
不等式一题matrix exponential question
Ask questions on Latin Hypercube sampling真心求教一道随机收敛的问题
矩阵乘积的特征值Re: 请教:这个不等式如何证明?
漫谈扭结(四)请教:这个不等式如何证明?[合集]
请教二元丢番图方程Re: is there a simple way to prove..?
相关话题的讨论汇总
话题: 不等式话题: 有类话题: correlated话题: variables