Question 7 Of 121 randomly selected men, X1 played tennis, whereas of M2 randomly selected women, X2

Question 7 Of 121 randomly selected men, X1 played tennis, whereas of M2 randomly selected women, X2played tennis. Let p1 and p2 denote the probabilities that a randomly selected man and woman,respectively, play tennis. You are interested in estimating the difference in the two probabilities,p1 — p2, and to this end you are considering using the following estimator: 63 = £ _ ?.”1 ”2a) Explain why you would use such an estimator. [3 marks]b) Is (9 an unbiased estimator? [6 marks] c) What is the mean square error of the estimator? [6 marks]