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Question 21 3 / 3 pts Suppose that X and Y are identically distributed with a mean of -3, a variance of 9, and Cov(X, Y) = 3. Find Corr(X, Y) O a. -3 O b. -1/3 O c. 0 Correct! O d. 1/3 O e. 1Question 27 0 / 3 pts Consider the following integral: I = foe x2/2 dx Use the following four Unif(0, 1) random numbers to compute a Monte Carlo estimate of I: 0.22 0.85 0.67 0.16 Here's the formula from class that ought to be used to calculate the estimate: 1 = ma EL 1 gla + (b - a) Ui). prrect Answer O a. 0.345 O b. 0.598 Du Answered O c. 0.702 O d. 0.996 https://gatech.instructure.com/courses/128642/quizzes/128199?module_item_id=751192 14/21 8/3/2020 ISyE 6644 - Summer 2020 - Midterm Test 1: Simulation and Modeling for Engineering and Science - ISYE-6644-OAN/001 O e. 1.382Question 28 0 / 3 pts Again, consider the integral: I = -- So e- /2dx. What is the exact solution to I? O a. 7 / 2 O b. 2/T prrect Answer O c. 0.341 Du Answered O d. 0.700 O e. 0.841Question 29 3/ 3 pts Suppose I inscribe a circle of radius 1/2 in a unit square. Now I randomly toss 200 darts in the square and 168 happen to land in the circle. Use this sample in conjunction with the example we did in class to give me an estimate of IT. O a. T O b. T / 2 https://gatech.instructure.com/courses/128642/quizzes/128199?module_item_id=751192 15/21 8/3/2020 ISyE 6644 - Summer 2020 - Midterm Test 1: Simulation and Modeling for Engineering and Science - ISYE-6644-OAN/001 O c. 3.04 O d. 3.18 Correct! O e. 3.36Question 30 3/ 3 pts Consider the linear congruential generator Xit1 = (5X; + 1)mod(8). If Xo = 3, calculate the pseudo-random number U2. O a. 0.062 Correct! O b. 0. 125 O c. 0.250 O d. 0.300 O e. 0.500