Week 3 Homework_ Simulation - ISYE-6644-OAN_O01_Q_ASY

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Apr 3, 2024

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3/22/24, 3:50 PM Week 3 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510405?module_item_id=3598390 1/4 Week 3 Homework Due Feb 2 at 11:59pm Points 7 Questions 7 Available Jan 26 at 8am - Feb 5 at 11:59pm Time Limit None This quiz was locked Feb 5 at 11:59pm. Attempt History Attempt Time Score LATEST Attempt 1 24 minutes 7 out of 7 Score for this quiz: 7 out of 7 Submitted Jan 30 at 7:43pm This attempt took 24 minutes. Question 1 1 / 1 pts Correct! a. -25 b. -5 c. 5 d. 25 Question 2 1 / 1 pts Correct! a. 34 (Lesson 2.11: Covariance and Correlation.) Suppose that the correlation between December snowfall and temperature in Siberacuse, NY is . Further suppose that 100 in and (degrees F) . Find (in units of degree inches, whatever those are). (Lesson 2.11: Covariance and Correlation.) If and both have mean and variance 4, and , find .
3/22/24, 3:50 PM Week 3 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510405?module_item_id=3598390 2/4 b. 36 c. 40 d. 41 Question 3 1 / 1 pts a. 0.027 b. 0.14 c. 0.86 Correct! d. 0.973 Denote . Then Denote . Then Question 4 1 / 1 pts a. 0.5 Correct! b. 0.1587 (Lesson 2.12: Probability Distributions.) You may recall that the p.m.f. of the Geometric distribution is If the number of orders at a production center this month is a Geom(0.7) random variable, find the probability that we'll have at most 3 orders. (Lesson 2.12: Probability Distributions.) Suppose the SAT math score of a University of Georgia student can be approximated by a normal distribution with mean 400 and variance 225. Find the probability that the UGA Einstein will score at least a 415.
3/22/24, 3:50 PM Week 3 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510405?module_item_id=3598390 3/4 This answer is (b). To see why, let denote his score and let denote a standard normal random variable. Then where you could've used the back of the book or the NORMSDIST function in Excel to look up that last probability. (Actually, this is a famous one, so you may have memorized it). c. 0.975 d. 0.8413 This answer is (b). To see why, let denote his score and let denote a standard normal random variable. Then where you could've used the back of the book or the NORMSDIST function in Excel to look up that last probability. (Actually, this is a famous one, so you may have memorized it). Question 5 1 / 1 pts a. Eastern Limit Theorem Correct! b. Central Limit Theorem c. Central Limit Serum d. Central Simit Theorem (simit is a tasty Turkish bagel) (b). Question 6 1 / 1 pts a. 0.1587 b. 0.3174 Correct! c. 0.6826 First of all, note that and Then by the CLT, we have Nor (1,1). Thus, (Lesson 2.13: Limit Theorems.) What is the most-important theorem in the universe? (Lesson 2.13: Limit Theorems.) If are i.i.d. from some distribution with mean 1 and variance 400, find the approximate probability that the sample mean is between 0 and 2.
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3/22/24, 3:50 PM Week 3 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510405?module_item_id=3598390 4/4 So the answer is (c). d. 0.8413 First of all, note that and Then by the CLT, we have Nor (1,1). Thus, So the answer is (c). Question 7 1 / 1 pts a. 13 b. Correct! c. 18 First of all, the same mean is . Then the sample variance is So that the answer is (c). d. 28 First of all, the same mean is . Then the sample variance is So that the answer is (c). Quiz Score: 7 out of 7 (Lesson 2.14: Estimation.) Suppose we collect the following observations: 7, , 1, 6. What is the sample variance?