1. [20 points] Sam just graduated from high school and is considering whether to start working immediately or to attend a 4-year university. He currently has a job offer that promises a life-time income of 2 million dollars. After graduating from the university, Sam can find a job with 4-million- dollar life-time income with probability 1/2 and a job with 2-million-dollar life-time income with probability 1/2. The total cost of attending the 4-year university is 0.2 million dollars. Sam cannot afford this cost on his own and must obtain a government loan with an interest rate of 20%. (a) Should Sam attend the university or not? Prove your answer. (b) All else the same, now suppose the university program is very challeng ing and Sam may have to drop out after the first semester with probability 1/2. If he drops out, he can only find a job with a life-time income of 1.5 mil- lion dollars. Attending the university for the first semester costs 0.01 million dollars. Again, the government loan rate is 20%. In this situation, should Sam attend the university? Prove your