Problem 4 (20+2 Points): Small Lotto "Small Lotto" is a lottery where: . tickets are numbered from 1 to 10 (10 total tickets possible) . one may buy multiple copies of the same ticket number . a single winning number is chosen uniformly at the end of each week. To win, a ticket must match the winning number . each winning ticket pays a dollar Consider each of the following strategies to buying 3 lotto tickets in the same week: . First: Buy ticket numbers 1, 2,3 . Pi: Buy ticket numbers 3, 1, 4 . Lucky 7: Buy ticket numbers 7, 7, 7 Identify which of the three strategies (there may be more than one) optimize the four criteria immediately below. Justify each response with one sentence. i Maximum total prize possible ii Maximum chance that one ticket wins iii Maximum expected total prize iv Minimum variance of the total prize v Extra Credit: Describe how you'd update your responses to include the "Uniform" strategy given below: . Uniform: Each ticket number is chosen independently and uniformly from all possible lottery numbers (repeats possible) (Please respond as a seperate "part v" so we can grade this section distinct from the other parts, thank you!) We use the term "total prize" to refer to the total prize money across all tickets