Please show all necessary steps.

(a) Let 1(X)=Var(X) be a risk measure associated with a random variable X. (i) Use a counter example to show that 1(X) is not monotonic in general. (ii) Check the translation invariance, homogeneity and subadditivity of 1(X). (b) Let 2(X)=E(X)+Var(X), where >0 is a constant. Check the monotonicity, translation invariance, homogeneity and subadditivity of 2(X). Is 2 a coherent risk measure