Consider the following example when answering (c)-(e). You want to buy a plane ticket to California and you will definitely buy a ticket this week. Each morning, you have to choose whether you will buy the ticket that day or not (day t = 1, 2, 3, ..., 7). The price of the ticket is either $50, $150, or $200 and you see this price online in the morning before you decide. If the ticket costs $200 on day i, then it will cost $200 on day i +1 with probability 0.5, it will cost $150 on day i+ 1 with probability 0.45, and it will cost $50 on day i +1 with probability r. Today (this morning, t = 1), you know the ticket price is $200. Your objective is to minimize your total expected cost and there is a terminal penalty cost of $500 for not buying your ticket before day t = 8. Using this information, please complete (c)-e). What is the missing value of x? i. 0.01 ii. 0.05 iii. 0.15 iv. 0.25 What best defines the states of the MDP? i. Let se e S denote the purchase decision on day t (c) (d) 1 (e) ii. Let st S denote the current day in the planning horizon iii. Let se ES denote the cost of the ticket on day t Which day corresponds to the terminal epoch? i. t=1 ii. t=4 iii. t=8