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Let be $x,y$ are two random variable. How I will be able to start demonstrate that if $$E(xy^*)=E(x)\cdot E(y^*)\rightarrow E((x-\mu_x)(y-\mu_y)^*)=0?$$

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? no understand your question – juaninf Nov 16 '12 at 2:25
Do you mean that $E((x-\mu_x)(y-\mu_y))=0$? – André Nicolas Nov 16 '12 at 2:31
ahhh sorry do you mean $E((x-\mu_x)(y-\mu_y)^*)=0$ – juaninf Nov 16 '12 at 2:38
In my lecture I don't understand Why the "$^*$" symbol – juaninf Nov 16 '12 at 2:40
Hint: Expectation is a linear operator: colloquially, the expectation of a sum is the sum of the expectations, but more formally, $E[aX+bY] = aE[X]+bE[Y]$. So, what does $E[(x-\mu_x)(y-\mu_y)]$ when you multiply out everything between $[$ and $]$ and use the linearity of the expectation operator? – Dilip Sarwate Nov 16 '12 at 2:53

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