Random vector X = (X 1,X 2,X3)T E R3 has multivariate normal distribution with parameters 4 1 0 E300 = (1,1,2)T, Var(X) = 1 1 0 0 0 2 (a) (2 points) Find P(2X2 > X1 + 3). (b) (1.5 points)Find matrix A E R2\" and vector p. E R2 such that for Y Cl=Bf A(X1,X3)T +,u it holds YTY ~ x20), where X2(2) denotes the chisquared distribution with 2 degrees of freedom. (Hint: (a) cf. exercise 3.5.14 in the textbook: nd vector a at aTX = 2X2 X1 and use the properties of the normal distribution. Similarly for part (b): nd a linear transformation of (X 1,X 3)T that leads to the required distribution.)