LA city planners are attempting to set a tax rate on unimproved residential real estate. The rate

will be on a per-square-foot basis. Suppose all of the lots under study are rectangular, with an

average width of 50 feet and an average depth of 80 feet. The standard deviation of the width

is 10 feet and the standard deviation of the depth is 11 feet. The proposed tax rate is $0.50 per

square foot.

(a) What is the average tax revenue per lot if the width of a randomly picked lot is always

independent of the depth?

(b) Now assume that the width and depth are not independent and that the correlation between

the width and depth is 0.8. What is the covariance between the width and depth?

(c) What is the average tax revenue per lot, assuming the width and depth are correlated as in

part (b)?