Question: Full Explanation Required: Question 1: Consider a discrete real random variable Y with realizations yk, k = 1, ..., n, attained with probabilities PK >

Full Explanation Required:

Question 1: Consider a discrete real random variable Y with realizations yk, k = 1, ..., n, attained with probabilities PK > 0, _ _PK = 1. Calculate the minimum of the fol- lowing functions Qla. f(x) = E[(Y - x) 2]. Q1b. g(x) = E[Y - x1]. Qlc. For a E (0, 1), h(x) = E[ max (a (Y - x), (1 -a)(x -Y) )]. Question 2: (Bonus question) For given three points a, b and c on the plane, find the point x which has the minimum sum of its Euclidean distances to a, b and c using the optimality conditions

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