Please answer the following question. Don't copy others answers, thank you!

Question 1 (10 marks) Let f(x) = ar' + br + c be a second degree polynomial (where a, b, c ( R are constants). (a) Find necessary and sufficient conditions on a, b and c so that the equation E[f(o X )] = ofE[f(X)] holds for all o ( R and all rvs X with finite E[X ]. (4 marks) (b) Find necessary and sufficient conditions on a, b and e so that the equation Elf (X + 8)] = E[f(X)] holds for all 8 ( 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)