(Solved): Question 2 20 pts Ann and Bruce play a game of alternating turns in which each turn consists of a ...

Question 2 20 pts Ann and Bruce play a game of alternating turns in which each turn consists of a single roll of a fair six-sided die. Ann rolls first. The first person to roll a number that is greater than two times the number that was last rolled (by their opponent) wins the game, and the game ends then. (a) What is the probability that Ann wins the game? 5 pts (b) What is the expected value of N, the number of turns until the game ends? 5 pts (c) What is the moment-generating function of N, m(t) = Ee¹N? 6 pts (d) Ann suspects that Bruce's die is on average rolling 6 more often than hers. They decide to perform an experiment to test this against the null hypothesis that Bruce's die rolls 6 no more often than hers. Write down a formula for an appropriate test statistic and its approximate distribution under the null hypothesis. In 120 rolls of Ann's die, 18 rolls were 6. In 100 rolls of Bruce's die, 22 rolls were 6. What is the value of the test statistic and the p-value? Is this strong evidence that Bruce's die rolls 6 more often than Ann's? 4 pts