5 Andy and Novak are playing a tennis match. I think Novak is definitely going to win, but my friend is not so sure. I o

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5 Andy And Novak Are Playing A Tennis Match I Think Novak Is Definitely Going To Win But My Friend Is Not So Sure I O 1 (202.27 KiB) Viewed 39 times

5 Andy and Novak are playing a tennis match. I think Novak is definitely going to win, but my friend is not so sure. I offer to give my friend £10 if Andy wins, as long as my friend gives me £20 if Novak wins. Suppose that the probability that Novak wins is 0.8. (i) Show that the expected value of my winnings, W, is £14 and the standard deviation of W is £12. (4 marks) Suppose that we repeat this bet a total of 25 times, i.e., we bet on each of 25 matches between Andy and Novak. Assuming that Novak's probability of winning remains 0.8 and my winnings from each bet are independent, calculate the mean and standard deviation of my total winnings T, where T = w; and W; is my winnings from the įth bet. (3 marks) 25 = 1 (iii) Use Chebyshev's inequality to give a lower bound for P(240 <T < 460). (4 marks) (iv) Use a Normal approximation to calculate P(240 <T < 460), carefully explain- ing your answer. You may assume that you do not need to use a continuity correction. You are given the following R output to complete the calculation. > pnorm(1.8333) [1] 0.966621 (4 marks)