The bivariate random variables X and Y have joint probability distribution specified by the following table:
| | y=1 | y=2 | y=3 | y=4 |
|---|---|---|---|---|
| x=1 | 0.05 | 0.10 | 0.10 | 0.01 |
| x=2 | 0.15 | 0.25 | 0.20 | 0.05 |
| x=3 | 0.01 | 0.03 | 0.04 | 0.01 |
Please provide all answers to the following to three decimal places.
(a) Find the expectation of XY.
4.1800
(b) Find the covariance Cov(X, Y) between X and Y.
.026
(c) What is the correlation between X and Y?
.053
(d) Suppose the random variables X and Y above are connected to random variables U and V by the relations
X = 9U + 3
Y = 3V + 9
What is the covariance Cov(U, V)?
(e) What is the correlation between U and V?