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Let X1, X2, ..., Xn be a random sample of n iid random variables from a distribution with probability density function: fx (x, Y) : -x/(BY), x20, BY where Y > 0 is a parameter, and B > 0 is a constant. Using the formulae for the first two population moments E (X) = By, E(X2) = 2BY, answer the following questions: a) [10 marks] Consider the estimator Y = X = _ _ _Xi. Is it a sufficient estimator for Y? Justify your answer. b) [5 marks] Consider the estimator Yo = ax. For what value of a is the estimator Y, unbiased for y? Justify your answer. c) [10 marks] For the value a from part b), is the estimator Yo an efficient estimator for y? Justify your answer. d) [5 marks] Provide the definition of consistent estimator and explain its meaning. Is estimator Ya a consistent estimator? Justify your