4. (10 points) Professor Minwoo decides to give a prize of $400 to twenty students in our class. Now, the elated students are deciding how to divide the $400 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $98 to first person and $76 to the second is different from giving $76 to the first person and $98 to the second. (a) How many ways are there to divide up the $400, such that each gets at least $15? (b) Assume that the $400 is randomly divided up, with all of the possible allocations counted in (a) equally likely. Let Z represent the amount the first person receives. State the state space Sz. (c) Considering the condition of (a) and state space in (b), find the the expected amount of money that the first person receives. You can leave your answer as a sum. 4. (10 points) Professor Minwoo decides to give a prize of $400 to twenty students in our class. Now, the elated students are deciding how to divide the $400 up between them. Assume that whole dollars are used, not cents. Also, for example, giving $98 to first person and $76 to the second is different from giving $76 to the first person and $98 to the second. (a) How many ways are there to divide up the $400, such that each gets at least $15? (b) Assume that the $400 is randomly divided up, with all of the possible allocations counted in (a) equally likely. Let Z represent the amount the first person receives. State the state space Sz. (c) Considering the condition of (a) and state space in (b), find the the expected amount of money that the first person receives. You can leave your answer as a sum