Question: The random variables X and Y have joint probability distribution specified by the following table: y=1 y=2 y=3 x=1 0.30 0.05 0.00 x=2 0.05 0.20

The random variables X and Y have joint probability distribution specified by the following table:

	y=1	y=2	y=3
x=1	0.30	0.05	0.00
x=2	0.05	0.20	0.05
x=3	0.00	0.05	0.30

Please provide all answers to the following to three decimal places. (a) Find the expectation of XY. (b) Find the covariance Cov(X,Y) between X and Y. (c) What is the correlation between X and Y? (d) Suppose the random variables X and Y above are connected to random variables U and V by the relations

X=6U+7 Y=8V+9

What is the covariance Cov(U,V)? (e) What is the correlation between U and V?

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