38. Three different roads feed into a particular freeway entrance. Suppose that during a xed time period, the number of cars coming from each road onto the freeway is a random variable, with expected value and standard deviation as given in the table.

Road 1 Road 2 Road 3 Expected value 800 1000 600 Standard deviation 16 25 18

a. What is the expected total number of cars entering the freeway at this point during the period?

(Hint: Let Xi  the number from road i.)

b. What is the variance of the total number of entering cars? Have you made any assumptions about the relationship between the numbers of cars on the different roads?

c. With Xi denoting the number of cars entering from road i during the period, suppose that Cov(X1, X2)  80, Cov(X1, X3)  90, and Cov

(X2, X3) 100 (so that the three streams of traf c are not independent). Compute the expected total number of entering cars and the standard deviation of the total.