Week 10 Homework Simulation Overview ISYE 6644 OAN O01 Q ASY Questions And Correct Answers |100% Verified |Guaranteed Success | update

Question 1 1 / 1 pts (Lesson 7.12: The Box-Muller Method.) Suppose and are i.i.d. Unif(0,1) with and . Use the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variate. Don't forget to use radians instead of degrees! a. -0.326 b. 0 Correct! c. 0.326 d. 0.663 e. 1.96 Box-Muller immediately gives the following Nor(0,1) random variate: To obtain the realization of the Nor($-$1,4), we simply apply the transform which is choice (c).  Question 2 1 / 1 pts (Lesson 7.13: Generating Order Statistics.) Consider i.i.d. Exp( ) random variables , and let . How can we generate using just one PRN? 3 a. b. Correct! c. d. /4 e. 1 3/28/25, 5:50 PM 2 e. 1 /4 denote the Exp( ) c.d.f. Recall that the inverse is a fact that we'll use in a minute. Meanwhile, as also explained in class, the c.d.f. of $Y$ is Now, by inverse transform, , and so . This implies that , and thus where the last equality follows from . This is choice (c).  Question 3 1 / 1 pts (Lesson 7.14: Multivariate Normal Distribution.) Suppose I have a matrix . Find the lower triangular matrix such that and tell me what the entry is (use the results from class). a. -1 Correct! b. -0.7071 c. 0 d. 0.3536 e. 1 From our class notes on multivariate normal RV generation, the Cholesky matrix is Therefore, the correct answer is (b).  Question 4 0 / 1 pts (Lesson 7.16: Nonhomogeneous Poisson Processes.) Suppose that the arrival pattern to a parking lot over a certain time period is an NHPP with . Use simulation to find the probability that there will be exactly 3 arrivals between times and . You Answered a. 0 Correct Answer b. 0.195 c. 0.5 Let F 3/28/25, 5:50 PM d. 0.805 /4 e. 1 2 3/28/25, 5:50 PM Week 10 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY 3 /4 I'll give the analytical solution. First of all, the number of arrivals in that time interval is Thus, This is answer (b).