Answer to Question #226079 in Statistics and Probability for Carrie

Question

f the coefficient of correlation is r D 0:81; the variances of X and Y are respectively, 20 and 25;

then the covariance cov .x; y/ or Sx y must be

1. 405

2. 90:56

3. 1:81

4. 18:11

5. 76:27

Answer 1

The covariance can be calculated as follows:

$r=\frac{Cov(X,Y)}{\sqrt{Var_X \times Var_Y}} \\ 0.81 = \frac{Cov(X,Y)}{\sqrt{20\times 25}} \\ Cov(X,Y) = 0.81 \times 22.36 =18.11$

Answer: option 4. 18.11