1112 Given the following jointlyordered populations X 2 3 5

(11-12): Given the following jointly-ordered populations:

X ={ 2, 3, 5, 6, 9)

Y={10, 9, 8, 2, 1}

11. Find Cov(X,Y), Cov(Y,X), Cov(X,X)

12. Find Cov(Y,Y), rho(X,X), and rho(X,Y)

Solution

X ={ 2, 3, 5, 6, 9)

Y={10, 9, 8, 2, 1}

Step 2: Find the sum of every column to get:

X=25 , Y=30 , XY=108 , X2=155 , Y2=250

11) Cov(x,y) = XY/n -   X Y /n^2= 108/5-25(30)/5x5

= 21.6-30

= -8.4

Cov(Y,x) = Same as cov (x,y) = -8,4

Cov (x,x) = Var(x) = 155/5 -5^2

= 6

12) cov (y,y) = var(y) = 250/5 -36

= 14

rho (x,x) = 1

rho (x,y) = cov (x,y)/std dev x(std devY)

=-0.9165