Question

Let X, Y , and Z be random variables. Which one(s) of the following statements is/are true?

(a) if Cov(X, Y ) > Cov(Y, Z) then ρXY > ρY Z.

(b) if ρXY > ρY Z then σX < σZ.

(c) if ρXY > 0 then Cov(X, Y ) > 0.

Answer 1

We know for any two ramdom variables P and Q

a) TRUE

Exaplanation: Take

And ,

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b)TRUE

Explanantion:This can be seen from the previous example.

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c)TRUE

Explanation: From the above example of part a) we can clearly see that as ,if cov(X,Y)>0 then

and of course vaice versa

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