Consider the independent random variables , Yz, Y , where Y ,N N ( th , = 10 , 52 = 5 ) ; Y, N N (J = 8 62 = 5 ) ; Yz ~ N ( Mg = 15 , 5 2 = 5) (a) Give the matrix for each of the quadratic forus A Y Yz andY, (i ) Q = Y, + Y, + Yg (1 ) Q = ( Y, - 10 ) + ( Y 2 - 10 ) + ( Y , - 10 ) Citi ) Q 3 = E ( Y , - 8 ) 2 CN ) Q4 = ( Y , - 10 ) + ( 7 2 - 8) + (1 3 - 15 ) Give the probability law of the following random variables ! Ci) Y = Y, + Y2 + Y3 3 U. = Q for biblare i = 1 , 2, 3, 4 where Q,, Q Q, Ox are defined in part (a )