1. A taxi driver provides service in two zones of a city. Fares picked up in zone A will have destinations in zone A with probability 0.6 or in zone B with probability 0.4. Fares picked up in zone B will have destinations in zone A with probability 0.3 or in zone B with probability 0.7. The driver's expected pro?t for a trip entirely in zone A is 6; for a trip entirely in zone B is 8; and for a trip that involves both zones is 12. Find the taxi driver's average pro?t per trip.
2. Find the average premium received per policyholder of the insurance company of Example 4.27 if λ= 1/4 for one-third of its clients, and λ = 1/2 for two-thirds of its clients.