Suppose that 2 balls are randomly removed from an urn containing n red and m blue balls. Let X_i = 1 if the i^th ball removed is red, and let it be otherwise, i = 1, 2.

a. Do you think that Cov(X₁, X₂) is negative, zero, or positive.

b. Validate your answer to part (a). Suppose the red balls are numbered, and let Y_i equal if red ball number is removed, and let it be if that ball is not removed.

c. Do you think that Cov(Y₁, Y₂) is negative, zero, or positive.

d. Validate your answer to part (c).