Eric is an owner of a big firm and James applied for that firm. If James is smart, he will make $10 for Eric and Eric will pay him $7 (so that Eric's profit from James will be $3). If James is not-smart, he will make $4 for Eric and Eric will pay him $3 (so that Eric's profit from James will be $1). The probability that James is smart is 1/2. Actually, Eric does not know if James is smart or not and he will pay the average wage ($7+$3)/2=$5 and the expected profit for Eric would be $7-$5=$2. Then, professor Hahn opened a "Useless University (=ULU)" and he gives a degree only to the students who pass his difficult examination. In order to pass the examination, the students should take professor Hahn's class and the tuition is $1 per month. If the student is smart, it takes only 1 month for him to pass the exam. On the other hand, if the student is not-smart, it takes 5 months to pass the exam. We will assume that Eric can check if James passes the exam or not, but Eric cannot check how many months James took professor Hahn's class. Find out two Perfect Bayesian equilibria of this game, one separating and one pooling.