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# Georgia Institute Of Technology ISYE 6644 -Week 8 Homework_ Simulation and Modeling for Engineering and Science - ISYE-6644-OAN-GRADED A+

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Week 8 Homework Due Jul 14 at 11:59pm Points 10 Questions 10 Available after Jul 5 at 8am Time Limit None Attempt History Attempt Time Score LATEST Attempt 1 65 minutes 4 out of 10  Correct ... answers will be available on Jul 17 at 12am. Score for this quiz: 4 out of 10 Submitted Jul 10 at 4:24pm This attempt took 65 minutes. Question 1 1 / 1 pts (Lesson 7.10: Acceptance-Rejection --- Poisson Distribution.) Suppose that , , and . Use our acceptance-rejection technique from class to generate . (You may not need to use all of the uniforms.) a. N=0 b. N=1 c. N=2 d. N=3 e. N=47/10/2019 Week 8 Homework: Simulation and Modeling for Engineering and Science - ISYE-6644-OAN https://gatech.instructure.com/courses/52126/quizzes/55301 2/12 Define . We'll stop as soon as . Let's make the following convenient table. So we take N = 3, and the answer is (d). Incorrect Incorrect Question 2 0 / 1 pts (Lesson 7.11: Composition.) BONUS: It's Raining Cats and Dogs is a pet store with 60% cats and 40% dogs. The weights of cats are Nor(12,4), and the weights of dogs are Nor(30,25). How would we use composition to simulate the weight of a random pet from the store? (Let denote the standard normal c.d.f., and let 's denote PRN's.) a. b. c. If , then ; otherwise, d. If , then ; otherwise, 7/10/2019 Week 8 Homework: Simulation and Modeling for Engineering and Science - ISYE-6644-OAN e. If , then ; otherwise, By inverse transform, the weight of a cat all by itself is Similarly, the weight of a dog all by itself is . These facts eliminate choices (a), (c), and (e). In addition, (a) and (b) are some kind of mutant cat-dog, both of which sort of combine 0.6 of a cat with 0.4 of a dog; so those are wrong. What we really want is to take with probability 0.6, and otherwise . This is choice (d)! Incorrect Incorrect Question 3 0 / 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 BoxMuller to generate a single Nor(-1,4) random variate. Don't forget to use radians instead of degrees! a. -0.326 b. 0 c. 0.326 d. 0.663 e. 1.967/10/2019 Week 8 Homework: Simulation and Modeling for Engineering and Science - ISYE-6644-OAN 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). Incorrect Incorrect Question 4 0 / 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? a. b. c. [Show More]

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