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(a) (1?) Answer to the following statements: (i) State TWO assumptions required before inferring about the difference between two population means. (2 marks) (ii) Provide two examples of when researchers would be interested in studying the variance of two populations rather than the means or proportions. (3 marks) Let the customer waiting times, X (in hours), at a restaurant is modeled as an exponential random variable with parameter 21. Suppose that the prior density mction for ii. is given as follows _; fen4!\" . Five eustomers' waiting times are observed: x1 = 0.23,x2 = 0.80;; = 0.12,:4;1 = 0.35, .7:s = 0.50. Compute the posterior density function of it. [Hint I: yaleby dy = (aginil (6 marks)