An insurance company has a policy that covers losses due to theft of a particular type of high-value equipment. The policy has a deductible of $1,000 and a limit of $50,000 per occurrence. The frequency of thefts follows a Poisson distribution with a mean of 3 per year, and the amount of loss per occurrence follows a normal distribution with a mean of $30,000 and a standard deviation of $10,000. Assuming that the losses are independent and identically distributed, answer the following questions:

a) What is the expected value and the standard deviation of the amount of loss per occurrence?

b) What is the probability that a single theft will result in a loss that exceeds the policy limit?

c) What is the expected amount of loss per occurrence that will be covered by the insurance policy?