Covariance of centred random vairablesCovariance and Random VariablesConditional Covariance of Functions of Random VariablesRandom Variables and covarianceCovariance with transformations of random variablesCovariance inequality for $n$ exchangeable random variablescovariance of random variablesCompute covariance of dependent random variablesMinimal Covariance of random variables.Covariance of independent random variables.Covariance of Marshall-Olkin random variables
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Covariance of centred random vairables
Covariance and Random VariablesConditional Covariance of Functions of Random VariablesRandom Variables and covarianceCovariance with transformations of random variablesCovariance inequality for $n$ exchangeable random variablescovariance of random variablesCompute covariance of dependent random variablesMinimal Covariance of random variables.Covariance of independent random variables.Covariance of Marshall-Olkin random variables
$begingroup$
Let $X$ and $Y$ be two random variables, with $mathbbE(X)=mathbbE(Y)=0$.
Is it true that $mathbbE(XY)=0$ ? In other word, is it true that cov$(X,Y)=0$ ?
probability probability-theory expected-value
asked Mar 15 at 17:20
C.S.C.S.
235
$endgroup$
add a comment |
$begingroup$
Let $X$ and $Y$ be two random variables, with $mathbbE(X)=mathbbE(Y)=0$.
Is it true that $mathbbE(XY)=0$ ? In other word, is it true that cov$(X,Y)=0$ ?
probability probability-theory expected-value
asked Mar 15 at 17:20
C.S.C.S.
235
$endgroup$
add a comment |
$begingroup$
Let $X$ and $Y$ be two random variables, with $mathbbE(X)=mathbbE(Y)=0$.
Is it true that $mathbbE(XY)=0$ ? In other word, is it true that cov$(X,Y)=0$ ?
probability probability-theory expected-value
asked Mar 15 at 17:20
C.S.C.S.
235
$endgroup$
Let $X$ and $Y$ be two random variables, with $mathbbE(X)=mathbbE(Y)=0$.
Is it true that $mathbbE(XY)=0$ ? In other word, is it true that cov$(X,Y)=0$ ?
probability probability-theory expected-value
probability probability-theory expected-value
asked Mar 15 at 17:20
C.S.C.S.
235
asked Mar 15 at 17:20
C.S.C.S.
235
asked Mar 15 at 17:20
C.S.C.S.
235
asked Mar 15 at 17:20
C.S.C.S.
235
asked Mar 15 at 17:20
C.S.C.S.
235
235
add a comment |
add a comment |
1 Answer
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$begingroup$
It is not true.
Consider $$P(-1,-1)=P(1,1)=frac12$$
Then $E(X)=0=E(Y)$ but $E(XY)=1$.
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
It is not true.
Consider $$P(-1,-1)=P(1,1)=frac12$$
Then $E(X)=0=E(Y)$ but $E(XY)=1$.
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
$endgroup$
add a comment |
$begingroup$
It is not true.
Consider $$P(-1,-1)=P(1,1)=frac12$$
Then $E(X)=0=E(Y)$ but $E(XY)=1$.
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
$endgroup$
add a comment |
$begingroup$
It is not true.
Consider $$P(-1,-1)=P(1,1)=frac12$$
Then $E(X)=0=E(Y)$ but $E(XY)=1$.
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
$endgroup$
It is not true.
Consider $$P(-1,-1)=P(1,1)=frac12$$
Then $E(X)=0=E(Y)$ but $E(XY)=1$.
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
answered Mar 15 at 17:24
Siong Thye GohSiong Thye Goh
103k1468119
103k1468119
add a comment |
add a comment |
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