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.
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