(a) Let us consider a stack of 20 different reference books in the AMA library, labeled by book B1, B2, B20. We assume that, at each unit of time, only one book among B to B20 is selected and read by the student and it is then returned to the top of the stack. At each unit of time, the book Bi is selected with the probability Pi, i = 1, ..., 20, independent of the past and independent of the position. After a long period of time, i.e., all books have been selected already by the student, compute the expected position of the book selected by the student at random. - [10 marks] (b) At a graduation party 20 men take their ID cards and mix up on the table. Then they randomly select the cards and each man can only select one ID card. We say that a match occurs if a man selects his own ID card. What is the probability that there is no match for these 20 men? (a) Let us consider a stack of 20 different reference books in the AMA library, labeled by book B1, B2, B20. We assume that, at each unit of time, only one book among B to B20 is selected and read by the student and it is then returned to the top of the stack. At each unit of time, the book Bi is selected with the probability Pi, i = 1, ..., 20, independent of the past and independent of the position. After a long period of time, i.e., all books have been selected already by the student, compute the expected position of the book selected by the student at random. - [10 marks] (b) At a graduation party 20 men take their ID cards and mix up on the table. Then they randomly select the cards and each man can only select one ID card. We say that a match occurs if a man selects his own ID card. What is the probability that there is no match for these 20 men