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Let f(x) = ar- + br + c be a second degree polynomial (where a, b, c E R are constants). (a) Find necessary and sufficient conditions on a, b and c so that the equation Elf(oX )] = a"E[f(X)] holds for all o ( R and all rvs X with finite EX-]. (4 marks) (b) Find necessary and sufficient conditions on a, b and c so that the equation EIf (X + B)] = E[f(X)] holds for all B E R and all rvs X with finite E[X?). (4 marks) (c) Do parts (a) and (b) account for properties of a variance? Why and why not?. (2 marks)