An insurance company estimates that the annual number of car accidents for a group of drivers follows a Poisson distribution with a mean of 3 accidents per year. The company offers two insurance policies: Policy A with a premium of $100 per year and covers up to 2 accidents per year, and Policy B with a premium of $200 per year and covers up to 4 accidents per year. Assuming that the only cost to the company is the amount paid to policyholders for their claims, answer the following questions:

a) What is the expected value and the standard deviation of the number of accidents per year?

b) What is the probability that a driver with Policy A will have no claims in a year?

c) What is the expected amount of claims per year for a driver with Policy A?

d) What is the expected amount of claims per year for a driver with Policy B?