Suppose the multivariate random variable (Z1, Z2, Z3) has a standard Gaussian distribution on R3. Let the larger eigenvalue of the matrix V521 Z3 Z3 Z2 be A1 and the smaller one is called A2. a. [2 mark] Find a formula for A1 and A2 in terms of Z1, Z2, Z3. b. [1 mark] Define random variables X and Y by X=A1+A2 Y=A1A2. Write down the formula for X and Y in terms of Z1, Z2, Z3. c. [7 marks] Find the density function of %. [You should explicitly calculate any unknown constants] d. [4 marks] Find, for c > 1, the probability [P (A1 2 CA2)