An overworked math professor is considering a combined life insurance/long-term disability policy that costs $550 for one year of coverage. The policy pays out $120,000 in the event of his death, and $20,000 if he survives but misses more than 6 months of work for medical reasons (called “long-term disability”).
Based on the professor’s profile, it is estimated that he has a .986 probability of surviving with no long-term disability, a .012 probability of surviving but with a long-term disability, and a .002 probability of not surviving the year at all.
(a) Construct a probability distribution for the discrete random variable X representing the net value of this policy to the insurance company.