Problem: You plan to purchase dental insurance for your three remaining years in school. The insurance makes a one-time payment of $1,000 in case of a major dental repair(such as an implant ) or $100 in case of a minor repair (such as a cavity). If you don't need dental repair over the next 3 years, the insurance expires and you receive no payout. You estimate the chances of requiring a major repair over the next 3 years as 5%, a minor repair as 60% and no repair as 35%.

Required:

Question 1: Why is X= payout of dental insurance a random variable?

Question 2: Is X discrete or continuous? What are its possible values?

Question 3: Give the probability distribution of X.