Three different roads feed into a particular freeway entrance. Suppose that during a fixed time period, the num- ber of cars coming from each road onto the freeway is a ran- dom variable, with expected value and standard deviation as given in the table. Road 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 X = the number from road i.]

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

c. With .X, denoting the number of cars entering from road i during the period, suppose that Cov(X, X)=80, Cov(X1, X3)=90, and Cov(X2, X)=100 (so that the three streams of traffic are not independent). Compute the expected total number of entering cars and the stan- dard deviation of the total.