1 pts OT N O Let X = HAON Find the solution to XTy. 3 ,y 5 Select the most appropriate option. O 15 12 O 27 15 O [27 15] O [15 12] D Question 1 pts Five students from the previous year MBA class took jobs in rocket science after graduation. Four of these students reported their starting salaries: $95,000, $106,000, $106,000, $118,000. The fifth student did not report a starting salary. Based on this information, identify the correct statement from the following. Select the most appropriate option. O The median starting salary for all five students could be anywhere between $95,000 and $118,000. O The median starting salary for all five students is $106,000. The median starting salary for all five students is $106,500. O The median starting salary for all five students could be greater than $118,000.D Question 1 pts Let A = [2 -1 1] and B = [3 0 5 ]; A and Bare vectors. What is the solution for A + B? Select the most appropriate option. O [2 0 -1] O [6 0 5] 0 [5 1 4] 0 [5 -1 6] D Question 1 pts Let A = [2 1] and B = [3 0 5 ]. What is the solution for A - B? Select the most appropriate option. O [2 -3 1 -0 5] O [2 -3 1-0] O [11] O Vectors of different lengths cannot be subtracted D Question 1 pts Let A = [2 1 2]. What is 6A? Select the most appropriate option. O [6 2 6] O [ 12 6 12] O [8 6 8] O 14Question ' 1 pts The matrix form of the maximum likelihood estimator is w = (XTX)_1XTy , where: w is a vector of weights X is an n x cl matrix with n rows and (1' features. y is a column vector with n rows. Which of the following statements are true about this function? Select all options that apply. [I Superscript T is the transpose of the matrix. D Superscript -1 stands for the identity matrix' D m is a dx 1 vector. El 11; is a scalar. Question . 1 pts Let X : . Without doing the multiplication, what is X TX ? OIWOUI 1 Select the most appropriate option. 052 01 5035 33l2131l 571 052 01 5323 33i05171l 51 0 52 5035 01 l2131l33 51 0 12 1323 {14 i0541l33 51 D Question 1 pts OT O Let X = . Which solution would yield the correct result for 3 5 element an in the matrix solution of XT X ? Select the most appropriate option. O all = 25 + 0 + 9 + 25 O all = 2 * 1 +4*0+3*3+-1*5 O all = 2 * 5 +4*4+3*3+-1 *5 O all = 5 +0+9 -25 D Question 1 pts Let A = X" X = [4 . What is the correct representation of A -!? Select the most appropriate option. O Al 2 det ( A) -4 O 2 -3 1+2+4+3 -4 1 OA = 3 1+2-4+3 4 2 O Al = det (A) 2Questior. 1 pts Class Y had exams in Finance and Marketing last week. All 60 students in the class took both exams. The results were as follows: - Finance: mean = 25, standard deviation = 2 . Marketing: mean = 75, standard deviation = 12 . Correlation between score in Finance and same student's score in Marketing = 0.84 Mary, a student in class Y, scored a 30in Finance and a 90 in Marketing. Compare her performance on the two exams relative to the rest of the class. In particular, make a statement about which of her scores ranked higher compared to the other scores on the same exam. Select the most appropriate option. 0 Mary's score in Finance probably ranks higher than her score in Marketing. 0 Mary's score in Marketing probably ranks higher than her score in Finance. 0 Mary's scores on the two exams probably rank about equally high. Q We cannot make any comparison between the two scores. Question. 1 pts What's the relationship between: a) Height and weight b) Smoking cigarettes vs. lung cancer Select the most appropriate option. O a: Causation; b: Correlation O a: Causation; b: Causation O a: Correlation; b: Causation O a: Correlation; b: Correlation D Question 1 pts An inverse floater is a type of security whose payments move in the opposite direction of short-term interest rates. The security is ordinarily structured so that no matter how high interest rates rise, the payment cannot be negative, and no matter how low interest rates drop, the payment cannot exceed some specified cap, e.g., 7%. Consider the following specific case: if the prevailing short-term rate is X, the inverse floater pays Y = 100 x max(0.07 - X, O) on $100 of face value. (The notation "max(0.07 - X, O)" means use whichever is larger, 0.07 - X or 0.) Suppose the distribution of the short- term rate X at the next payment date is given by the following table: X 0.04 0.06 0.07 0.08 0.09 P(X=X) 0.30 0.20 0.20 0.15 0.15 Find the expected payment E[Y ]. Select the most appropriate option. O 0.8 O 1.1 O 1.5 O 1.8 D Question 1 pts A manufacturing process has a 3% defect rate. Inspectors catch 95% of defects but also fail 5% of non-defective parts. If we pick a part at random from all those that pass inspection, what is the probability that part is actually defective? Select the most appropriate option. O 5% O 3% O 0.16% O 0.5%D Question 1 pts If a, y E R and a, b E R, which of the following equations are true? Select all options that apply. buty = 6* by O x =0 (ab)I = albi D Question 1 pts Assume: Bo = -1.2 B1 = 0.5 B2 = 1.02 x1=1 x2 = 2 Then, what is the output when evaluating the following function? 1 +e(Bo+$121 + 82 12) Select the most appropriate option. O 0.79 O 0.69 O 0.85 O 0.89D Question 1 pts Find the limit of: limx--3 (x+3)4 Select the most appropriate option. 0 -1 0 1 D Question 1 pts Use the definition of a derivative to find f' (ac): f(a) = 5x2 + 5x + 2 Select the most appropriate option. O 10 0 8 O 10x + 5 O 5x2 + 5xD Question 1 pts Utilizing the derivative from above, find the the minimum y-value of the following function: f(ac) = 5x2 + 5x + 2 Select the most appropriate option. O 0.65 O 0.75 O 0.55 O 0.45 D Question 1 pts Ify = (22 + 1), find dy Select the most appropriate option. O 2 2 V(x2+1) O V( 2 2+ 1 ) O 2x V(x2+1) O V( 72 + 1)D Question 1 pts Find the domain of f iff (x, y, z) = In(y - x) + xycosz. Select the most appropriate option. O D = {(x, y, z) ER' |z > x] O D = {(x, 2) ER' |z > x} O D = {(x, y, z) ER'ly > x} O D = {(x, y, z) EN/z