5. Suppose that (X1,X2) follows a BVN(,), where =(1,2) and =(2222) with <1. Let X=(X1+X2)/2 and S2=(X1X)2+(X2X)2. [3] (a) Find the distribution of X1+X2. [5] (b) Prove that X1+X2 is independent of X1X2. [3] (c) Is X independent of S2 ? Justify your reasoning..