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Taking this table as an example of how would one be able to find E(XY) Table with numbers I know that if X and Y are independent then: $$E(XY) = E(X)*E(Y)$$

What method should be used if one doesn't know if X and Y are independent?

Thank you very much for your response.

(In this case, the answer is 12)

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Since you don't know if the variables are independent, just use the definition of expectation: $$E[XY]=\sum_{x,y}xyP(X=x,Y=y)=2\cdot 1 \cdot \frac{1}{8}+2\cdot 3\cdot \frac{1}{24}+...=12$$

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  • $\begingroup$ In fact, we know the variables are dependent, since $\mathsf P(X=4, Y=9)=0$. $\endgroup$ Commented Jan 24, 2019 at 0:29

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