An insurance company sells a one-year term life insurance policy to an 80-year-old woman. The woman pays a premium of $1,000. If she dies within one year, the company will pay $20,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 80-year- old woman will be alive one year later is 0.9516. Let be the profit made by the insurance company. Find the probability distribution and the expected value of the profit by hand. (6 points)