4. Gaussian level sets Let 2 = U AU T, where U is the orthogonal matrix U: [cos sin6 ] a sin 0 cos 9 0 = 7r/4, and A = diag(5, 1). Suppose that X N N01, 2) where p, = [2 3]T. (a) Sketch the boundary of 6 == {x ' (a: \"FE-Wm u) 5 H} where r = 1. Hint: If we change 3 r2 to = T2, the set C is an ellipse. Your sketch should indicate the center, lengths of major and minor axes, and angle between the major axis and LII-aXlS. Sketches may be hand drawn. (b) What is Pr(X E C)? Hint: Use the chisquared distribution and the following property of multivariate Gaussians: If X N N(u, E), and A is a matrix such that AX is well dened, then AX ~ N(A,u, AEAT)