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?

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The random variables X and Y have joint probability distribution specified by the following table:
y=1 y=2 y=3
x=10.30 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 = 2U + 2
Y = 3V + 8
What is the covariance Cov(U,V)?
(e) What is the correlation between U and V?
Transcribed Image Text:The random variables X and Y have joint probability distribution specified by the following table: y=1 y=2 y=3 x=10.30 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 = 2U + 2 Y = 3V + 8 What is the covariance Cov(U,V)? (e) What is the correlation between U and V?
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