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Let X1, ... , Xn be a random sample from gamma(a = 3, B = 1/11), and independently let Y1,..., Ym be a random sample form gamma(a = 4, B = 1/12). a) Using the statistics T = !-1 X; and W = L., Y; construct a pivot for 11/12. State the distribution of the pivot. b) Use the pivot in part (a) to construct a level 1 a confidence interval for 11/12, using equal tail probabilities. c) Suppose that we take samples from the two populations and 229, X, = 60 and 9. Y, = 140. Give a 90% confidence interval for 11/12 based on these data. Show your work Let X1, ... , Xn be a random sample from gamma(a = 3, B = 1/11), and independently let Y1,..., Ym be a random sample form gamma(a = 4, B = 1/12). a) Using the statistics T = !-1 X; and W = L., Y; construct a pivot for 11/12. State the distribution of the pivot. b) Use the pivot in part (a) to construct a level 1 a confidence interval for 11/12, using equal tail probabilities. c) Suppose that we take samples from the two populations and 229, X, = 60 and 9. Y, = 140. Give a 90% confidence interval for 11/12 based on these data. Show your work