How Do You Compute Var(X-2Y) When X and Y Are Not Independent?

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SUMMARY

The discussion centers on calculating the variance of the expression Var(X-2Y) where X and Y are random variables with given variances and a joint probability p(X,Y) = 1/3. The correct formula to use is Var(X-2Y) = Var(X) + 4Var(Y) - 2Cov(X,Y). Given that Var(X) = 9 and Var(Y) = 1, the computation requires determining Cov(X,Y) to finalize the variance calculation.

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hanelliot
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Studying for an intro course test and I have no one to compare it to right now.. any help would be appreciated.

Here is the question.

Q. Suppose X and Y are random variables such that p(X,Y)=1/3, Var(X) = 9 and Var(Y) = 1. Compute Var(X-2Y).

Since X and Y are not independent, we are using this formula: Var(X-Y) = Var(X) + Var(Y) - 2Cov(X,Y), correct?
So, Var(X-2Y) = Var(X) - 4Var(Y) - 2Cov(X,Y)? How do I proceed from here?
 
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Hi, you may want to clarify what exactly p(X,Y) means here.
 

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