11.13 A particular driver commutes between Hoboken (H) and Atlantic City (AC).

Every time the driver goes from H to AC, he drives using cruise control at a fixed speed, which is uniformly distributed between 55 and 65 miles per hour (mph). Every time he drives back from AC to H, he drives at a speed which is either 55 mph with probability 1/2 or 65 mph with probability 1/2.

a) In the long run, what proportion of his driving time is spent going from H to AC?

b) In the long run, what proportion of his driving time is spent at a speed of 65 mph?