An insurance company sells a $20,000 whole life insurance policy for an annual premium of $300. Actuarial tables show that a person who would be sold such a policy with this premium has a 0.001 probability of death during a one-year time period. If the policyholder lives, the company gets a profit of $500. If the policyholder dies, then the company loses $19,700, or in terms of profit, -$19,500. Let X be a random variable representing the insurance company's profit. (Hint: This is a discrete random variable problem. Check the textbook and problems for similar material.)
a. List the probability distribution using the table format. Remember that X stands for profits and that the probabilities must meet the conditions of a legal probability distribution, e.g., the sum of the probabilities must equal 1. (Hint: For each outcome of X, there is one probability.)
b. What is the probability that a randomly chosen person will live the one-year time period?
c. Find the expected value of the company's profits. What does this number mean?