Georgia Institute Of Technology ISYE 6644 Week 9 Homework - Spring 2021 Simulation - ISYE-6644-OAN_O01.

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Week 9 Homework - Spring 2021 Due Mar 26 at 11:59pm Points 18 Questions 18 Available Mar 15 at 8am - Mar 26 at 11:59pm 12 days Time Limit None This quiz was locked Mar 26 at 11:59pm. Attempt Histo... ry Attempt Time Score LATEST Attempt 1 26 minutes 17 out of 18 Score for this quiz: 17 out of 18 Submitted Mar 26 at 11:59pm This attempt took 26 minutes. Question 1 1 / 1 pts (Lesson 7.1: Introduction to Random Variate Generation.) Unif(0,1) PRNs can be used to generate which of the following random entities? Correct! Correct! f. All of the above --- and just about anything else! (f). Question 2 1 / 1 pts 1 of 11 4/5/2021, 5:41 PM(Lesson 7.2: Inverse Transform Theorem --- Intro.) If is an Exp( ) random variable with c.d.f. , what's the distribution of the random variable ? X λ F(x) = 1 − e−λx 1 − e−λX Correct! Correct! a. Unif(0,1) Note that , where the last step follows by the Inverse Transform Theorem. Thus, the correct answer is (a). 1 − e−λX = F(X) ∼ Unif(0, 1) Question 3 1 / 1 pts (Lesson 7.2: Inverse Transform Theorem --- Intro.) If is a Unif(0,1) random variable, what's the distribution of ? U − λ1 ln(U) Correct! Correct! d. Exp(λ) Since and are both Unif(0,1) (by symmetry), we have where the last step follows from Lesson 2's Inverse Transform Theorem example. Thus, the answer is (d). U 1 − U − λ1 ln(U) ∼ − λ1 ln(1 − U) ∼ Exp(λ), [Show More]

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