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Question 1. [15 marks] Let X = [X1, X2] denote a realization of a bivariate Gaussian random vector. Assume that, the mean vector E (X) and covariance matrix _ are as follows, respectively, E(X = E = (1) where p is known and u is an unknown mean parameter of interest. (a). [5 marks ] Find a 1-dimensional sufficient statistic T for the unknown parameter M. (b). [5 marks ] Show that X1 is an unbiased estimator of the unknown parameter /. (c).[5 marks ] Derive the conditional expectation E X1 7). Then show that it is also an unbiased estimator of u and that its variance is lower than that of X1