Georgia Institute Of Technology ISYE 6644 Week 11 Homework_ Simulation - ISYE-6644-OAN.

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Week 11 Homework Due Nov 10 at 11:59pm Points 9 Questions 10 Available after Nov 1 at 8am Time Limit None Attempt History Attempt Time Score LATEST Attempt 1 110 minutes 6 out of 9 Score for thi... s quiz: 6 out of 9 Submitted Nov 3 at 1:12pm This attempt took 110 minutes. Question 1 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, Y You Answered ou Answered d. If , then ; otherwise, orrect Answer orrect Answer e. If , then ; otherwise, 12/7/2019 Week 11 Homework: Simulation - ISYE-6644-OAN https://gatech.instructure.com/courses/75320/quizzes/69201 2/8 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)! Question 2 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 BoxMuller to generate a single Nor(-1,4) random variate. Don't forget to use radians instead of degrees! a. -0.326 b. 0 Correct! 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). This study source was downloaded by 100000827039679 from CourseHero.com on 07-14-2021 09:44:32 GMT -05:00 https://www.coursehero.com/file/62616118/Week-11-Homework-Simulation-ISYE-6644-OANpdf/ This study resource was shared via CourseHero.com12/7/2019 Week 11 Homework: Simulation - ISYE-6644-OAN https://gatech.instructure.com/courses/75320/quizzes/69201 3/8 Question 3 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? a. b. Correct! Correct! c. d. e. Let F 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). [Show More]

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