Consider a bivariate probability distribution for random variables x and y as below. Both x and y have 3 possible values (1, 2, and 3). Use the probability
distribution in the table and compute the following:
y
x 1
2.
3
3
Total
1
0.1
0.2
0.15
0.45
2
0.2
0.1
0.05
0.35
3
0.05
0.05
0.1
0.20
Total 0.35
0.35
0.3
1.00
(1) expected value of x (4 points)
(2) variance of x (6 points)
(3) expected value of y (4 points)
(4) variance of y (6 points)
(5) Suppose Var(x+y)=2, compute covariance of x and y (4 points)
(6) Compute the correlation coefficient between x and y (4 points)