Cov(X,Y)=E(XY)-E(X)E(Y), but what should I do with this? Suppose the covariance

Question

Cov(X,Y)=E(XY)-E(X)E(Y), but what should I do with this?

Suppose the covariance between age and number of friends calculated using the 4,000 users (with no missing values) is 20. If you replace the missing values for age with the average age of the 4,000 users, would the covariance between age and number of friends increases, decreases, or stays the same (as 20)? Assume that the average number of followers for all 5,000 users is the same as the average for 4,000 users. To obtain full credit, you must show your proof clearly

Explanation / Answer

If you replace the missing values with the average (i.e. E(X) or E(Y)) , then it does not change E(X) or E(Y) and E(XY). So the final value also does not change. So covariance remains constant. (i.e. 20)

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