20. Suppose that X ~ Nn(a, o'I) where a is a nonzero n-vector of constants. Let b represent another nonzero n-vector. Define Pa = aa /(a a) and Pb = bb / (bb). (a) Determine the distribution of x/ Pax/o2. (Simplify as much as possible here and in all parts of this exercise.) (b) Determine the distribution of x Pbx/62. (c) Determine, in as simple a form as possible, a necessary and sufficient condition for the two quadratic forms in parts (a) and (b) to be independent. (d) Under the condition in part (c), can the expressions for the parameters in either or both of the distributions in parts (a) and (b) be simplified further? If so. how? 22. Suppose that x ~ Nn(lu, o2[(1 - p)I + pJ]) where n 2 2, -00 0, and 0