To approximate: The value of the integral ∫ 0 48 1 + ( cos x ) 2 d x to within 10 − 4 .

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Consider the following false statement: For all integers a and b, if ab = 1 (mod 8), then a = 1 (mod 8) or b = 1 (mod 8). (a) Which of the following could be used as a counterexample. Select all that apply. a = -7 and b = −7 a = 1 and b = 23 ☐ a = 3 and b: = −5 ☐ a = 4 and b = 6 □ a = −1 and b = −9

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Chapter 4.4, Problem 21ES

To determine

To approximate: The value of the integral ∫0481+(cosx)2dx to within 10−4.

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Consider the following false statement: For all integers a and b, if ab = 1 (mod 8), then a = 1 (mod 8) or b = 1 (mod 8). (a) Which of the following could be used as a counterexample. Select all that apply. a = -7 and b = −7 a = 1 and b = 23 ☐ a = 3 and b: = −5 ☐ a = 4 and b = 6 □ a = −1 and b = −9

A classification study involving several classifiers was carried out. After training and the usual validation step, the following table shows results for classifiers tried. In below, classifiers are identified as M1, M2 and so on. Sensitivity Specificity M1 0.82 0.82 M2 0.92 0.72 M3 0.72 0.92 M4 0.46 0.47 M5 0.03 0.16 M6 0.13 0.02 M7 0.33 0.64 M8 0.72 0.24 M9 0.47 0.82 M10 0.06 0.84 The following list has statements about the classifiers. In the list, there is a single incorrect statement. Please identify the incorrect statement. Hint 1: recall that a classifier dominates another if both performance measures are better. Hint 2: to help you visualize and compare classifiers, you may want to plot the classifier data in a ROC graph (which will not be submitted). Select one: Qa. O b. Oc. d. By swapping zeroes and ones, M5 can be worsened M8 does not dominate M9 M1 dominates all of M4, M5 and M6 M1 is a good classifier ? e. By swapping zeroes and ones, the performance of M4 does not change…

Consider the following training data, shown below before centering. XY 1 0 1 1 1 1 1 1 00 1 1 1 0 0 1 1 1 0 1 1 This data set will be analysed after centering all columns (not scaling). In what follows, the centered data columns are referred to as X and Y. Using these centered columns, we have the following quantities: XTX = 24/11 = 2.1818; XTY = 13/11 = and YTY = 24/11 = 2.1818. Ridge regression Q1 For 2 = R AR = 1.1818 0.56, compute and write in the provided space the ridge estimate ẞ (0.56). Use decimal numbers, not fractions. Q2 Using the ridge estimate ẞ (0.56) you just computed, determine the percentage of shrinkage achieved with respect to the squared L2 norm. That is, compute the shrinkage using || (0.56)||||||with the OLS estimate. In the provided space, write the shrinkage as percentage between 0 and 100 with decimal values. Lasso AR Q3 The following are several expressions for the lasso estimate: (2) = 0.5833 * (1 - 0.84622); L L (a) = 0.5833 * (1 -0.78572); (A) = 0.5417 *…