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I am a PhD student in Economics, I am reading a paper on statistics, and the author states the following proposition without proof. My question is is it correct? Do we need to impose more conditions to get the result？ Thanks!!!

Suppose x and y are random variables. If

(1) E[f(x,y)]=0

(2) f(x,y) and g(x,y) are increasing in x.

(3) f(x,y) and g(x,y) are decreasing in y.

Then

COV( f(x,y), g(x,y) )>0.

:wave:

Suppose x and y are random variables. If

(1) E[f(x,y)]=0

(2) f(x,y) and g(x,y) are increasing in x.

(3) f(x,y) and g(x,y) are decreasing in y.

Then

COV( f(x,y), g(x,y) )>0.

:wave:

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