3.30 Expected travel distances in a two-city area Consider the cities of Camville and Bigton, which are separated by the River Charlie. Only the 1-mile-long Haywire Bridge connects the two towns. The layout of the cities is shown in Figure P3.30. The population of each of the two cities is uniformly distributed throughout the cities. Camville has a density of _c people per square mile; Bigton's density is _b people per square mile.

a. Find the expected travel distance between two randomly selected people in Camville; find the expected distance between two randomly selected people in Bigton.

b. Find the expected distance between a randomly selected person in Camville and a randomly selected person in Bigton.

C. Find the expected distance between two randomly selected people in the greater Camville-Bigton metropolitan area.

d. Find the expected distance between two randomly selected people, one from each town, assuming that one can cross the River Charlie at any point along the _B miles of Bigton that run along the river. By how much does your answer differ from your answer in part (b) ?

e. Compute numerical values for all the questions above assuming that
i. _B = 4 miles                               ii. _B = 2,000 people/square mile
   _c = 6 miles                                  _c = 1,000 peoplel/square mile
    u = 2 miles
     v = I mile
W_B = 5 miles
W_c = 3 miles