11. Applications [60 points total] 1 Note:[a b] = 1 [ d 4;] C d ad bc C a A. [12 points] The following problems related to basic linear algebra and statistics are independent with each other. (a) 2*3+4*5+2*3 can be expressed as a multiplication of two vectors. What are the two vectors? (b) If you have a sample of {4, 3,2}, compute the mean and standard deviation (c) The midterm election is coming, and to a large extend, the future market performance depends on which party becomes majority in the House. Historically, the market return was 5% a year after an Republicans take the majority, and 3% if the Democrats keep the majority. Suppose you are predicting that the likelihood for the Democrats to win is 70%, what market return would you expect to see next year? (d) If the estimated univariate model is given as y = 3 + 2 x+ u, and i = 1.5, 37 = 6, what should be the average of the estimated residuals? In this section, you need the following critical values at a a=5% significant level: Df 60 >120 ta, Df: 1.67 1.66 t a/2, Df: 2.00 1.98 Fa, 1,DF 4.00 3.92 Fa, 2, DF: 3.15 3.07 The test statistics for a single restriction and the joint test are: t = (RB-q) F = (e.'ex - e'e)/J VS [R(X'X) 'R'] e'e/(n - K) ~ FJ.n-K