Refer to the Canadian Journal of Civil Engineering (Jan. 2013) study, Exercise 6.5.

Data from Exercise 6.5

Refer to the Canadian Journal of Civil Engineering (Jan. 2013) investigation of the use of variable speed limits to control freeway traffic congestion. Recall that the study site was an urban freeway divided into three sections with variable speed limits posted in each section. The probability distribution of the optimal speed limit for each of the three sections was determined. One possible set of distributions is as follows (probabilities in parentheses). Section 1: 30 mph (.06), 40 mph (.24), 50 mph (.24), 60 mph (.46); Section 2: 30 mph (.10), 40 mph (.24), 50 mph (.36), 60 mph (.30); Section 3: 30 mph (.15), 40 mph (.18), 50 mph (.30), 60 mph (.37). Consider a randomly selected vehicle traveling through the study site at a randomly selected time. For this vehicle, let X represent the section and Y represent the speed limit at the time of selection.

a. Find E(X). Interpret this result.

b. Find E(Y). Interpret this result.