14.6.2. Covariance

Try these first

1. 1.

   What does a covariance of zero imply about two random variables?

   Hint

   Think about their linear relationship.

2. 2.

   Write the formula for covariance.

   Hint

   Consider what the expected values imply.

3. 3.

   What does a covariance of zero indicate about two random variables?

   • They are independent
   • They are uncorrelated
   • They are dependent

   Hint

   Focus on their relationship in terms of correlation.

4. 4.

   If Cov(X, Y) > 0, what does this signify?

   • True
   • False

   Hint

   Consider how the variables influence each other.

5. 5.

   Given the dataset X = [2, 4, 6] and Y = [1, 3, 5], calculate Cov(X, Y) and discuss its implications.

   Hint

   Use the covariance formula and fill in steps for clarity.

6. 6.

   Discuss how covariance changes if we double the values of variable Y in the previous challenge problem. Calculate the new covariance.

   Hint

   Calculate each step and see how the multiplication affects the covariance.