Question

3. Recreate the grid of formulas for mean/expected value, variance, covariance, and correlation. Arrange the formulas in four columns: theory (expected value format), when you have the probabilities, when you have the entire population, and when you have a sample. I suggest using landscape orientation.

4)

4. Find the covariance of X and Y below. Note that the outcomes are in bold type and the probabilities are in italics.

			Y
		-1	0	1
	0	0.1	0.1	0.1 0.3
X	1	0.1	0.2	0.1 0.4
	2	0.1	0.1	0.1 0.3

                                         0.3            0.4         0.3

E(X) = 0 * 0.3 + 1 * 0.4 + 2 * 0.3 = 1    E(Y) = -1 * 0.3 + 0 * 0.4 + 1 * 0.3 = 0

X         Y         x-mean                        y-mean                        prob     3-way product

0          -1         -1                     -1                     0.1       0.1

1          -1         0                      -1                     0.1       0

2          -1         1                      -1                     0.1       -0.1

0          0          -1                     0                      0.1       0

1          0          0                      0                      0.2       0

2          0          1                      0                      0.1       0

0          1          -1                     1                      0.1       -0.1

1          1          0                      1                      0.1       0

2          1          1                      1                      0.1       0.1

                                                                                    0 = Cov(X,Y)

Answer 1