Week 2 Knowledge Checks: Calculus and Numerical Methods

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 1 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring) Due No due date Points 22 Questions 22 Time Limit None Allowed Attempts Unlimited Attempt History Attempt Time Score LATEST Attempt 1 19,698 minutes 21 out of 22 Submitted Jan 27 at 10:47pm Take the Quiz Again 1 / 1 pts Question 1 Optional: Week 2 Module 2 Lesson 1 Question 1 If , find the derivative a. b. c. Correct! Correct! This follows since We could also have used the chain rule,

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 2 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 d. This follows since We could also have used the chain rule, 1 / 1 pts Question 2 Optional: Week 2 Module 2 Lesson 1 Question 2 If , find the derivative a. b. Correct! Correct! By the chain rule, . c. d. e. I'm from UGA - I'm scared of math, and I don't know!

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 3 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 By the chain rule, . 1 / 1 pts Question 3 Optional: Week 2 Module 2 Lesson 2 Question 1 Which of the following methods cannot be used to find the zeroes of a complicated function? a. trial-and-error b. bisection c. Newton's method d. Newman's method acting Correct! Correct! 1 / 1 pts Question 4 Optional: Week 2 Module 2 Lesson 2 Question 2 BONUS. Use your favorite numerical method to solve a.

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2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 4 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 b. Correct! Correct! Of course, you can easily solve for ... on your calculator. But let's do this problem via the bisection method. (You can also use Newton's method, which might be quicker.) After a few more iterations, and you’ll indeed see that this thing appears to be converging to ... c. d. is an imaginary number

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 5 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 Of course, you can easily solve for ... on your calculator. But let's do this problem via the bisection method. (You can also use Newton's method, which might be quicker.) After a few more iterations, and you’ll indeed see that this thing appears to be converging to ... 1 / 1 pts Question 5 Optional: Week 2 Module 2 Lesson 3 Question 1 Find . a. b. c. d. Correct! Correct!

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 6 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 We have We have 1 / 1 pts Question 6 Optional: Week 2 Module 2 Lesson 3 Question 2 BONUS. Find a. b. Correct! Correct! This is tricky. You have to use integration by parts with and (using the notation of the notes). Then

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2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 7 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 c. d. This is tricky. You have to use integration by parts with and (using the notation of the notes). Then 1 / 1 pts Question 7 Optional: Week 2 Module 2 Lesson 3 Question 3 BONUS. Find . (Hint: this problem will make you so sick, you'll have to go to the...? ) a. Correct! Correct!

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 8 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 If we let and g(x)=sin(x), then and , so that seems to get us into a 0/0 issue. Thus, we'll need to employ L'Hôspital's rule (hence the Hint): b. c. d. Undetermined If we let and g(x)=sin(x), then and , so that seems to get us into a 0/0 issue. Thus, we'll need to employ L'Hôspital's rule (hence the Hint): 1 / 1 pts Question 8 Optional: Week 2 Module 2 Lesson 4 Question 1 Which of the following is not an integration method discussed in this lesson? a. Riemann sums b. Newmann sums Correct! Correct!

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 9 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 Never heard of it! c. Trapezoid Rule d. The Monte Carlo method Never heard of it! 0 / 1 pts Question 9 Optional: Week 2 Module 2 Lesson 4 Question 2 How does a mathematician capture a wild man-eating zoid? Select all that apply. a. You catch a zoid ou Answered ou Answered b. You capture a zoid ou Answered ou Answered c. You trap a zoid Correct! Correct! d. Trick question! It's always best to avoid a zoid altogether! orrect Answer orrect Answer 1 / 1 pts Question 10 Optional: Week 2 Module 2 Lesson 4 Question 3

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2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 10 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 Find the approximate value of the integral using the lesson's form of the Riemann sum with , specifically, a. b. Correct! Correct! I admit this isn't a great answer (not very close to the true integral of ). We would've done better if had been bigger or if we had used the midpoint of each interval instead of the right endpoint. Oh well. c. d. I admit this isn't a great answer (not very close to the true integral of ). We would've done better if had been bigger or if we had used the midpoint of each interval instead of the right endpoint. Oh well. 1 / 1 pts Question 11 Week 2 Module 2 Lesson 5 Question 1

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 11 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 Toss a 4-side die twice (you know, one of those goofy Dungeons and Dragons pyramid dice things). Assuming the die is numbered what's the probability that the sum will equal ? a. b. c. d. Correct! Correct! Each of has probability of turning up on a particular toss. Thus, Each of has probability of turning up on a particular toss. Thus, 1 / 1 pts Question 12 Week 2 Module 2 Lesson 5 Question 2 TRUE or FALSE? is a legitimate probability density function. True False Correct! Correct!

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 12 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 In order to be a legit p.d.f., f(x) must integrate to 1; but lo and behold. . . ☹ In order to be a legit p.d.f., f(x) must integrate to 1; but lo and behold. . . ☹ 1 / 1 pts Question 13 Week 2 Module 2 Lesson 6 Question 1 Suppose is a continuous random variable with cumulative distribution function . What is the distribution of the nasty random variable ? a. Normal b. Unif (0,1) Correct! Correct! This is simply the amazing Inverse Transform Theorem. c. Exponential d. Weibull

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2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 13 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 This is simply the amazing Inverse Transform Theorem. 1 / 1 pts Question 14 Week 2 Module 2 Lesson 6 Question 2 Suppose is a Unif (0,1) random variable. Name the distribution of a. Normal b. Unif (0,1) c. Exponential Correct! Correct! This is a consequence of the Inverse Transform Theorem. d. Weibull This is a consequence of the Inverse Transform Theorem. 1 / 1 pts Question 15 Week 2 Module 2 Lesson 6 Question 3 BONUS: TRUE or FALSE? is a prime number..

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 14 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 True Correct! Correct! Amazingly, it's TRUE! Fun Fact: It's called a "Mersenne prime", because it has the form where itself is prime. False Amazingly, it's TRUE! Fun Fact: It's called a "Mersenne prime", because it has the form where itself is prime. 1 / 1 pts Question 16 Week 2 Module 2 Lesson 7 Question 1 Suppose is a continuous random variable with p.d.f. Find a. b. Correct! Correct! c. d.

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 15 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 1 / 1 pts Question 17 Week 2 Module 2 Lesson 7 Question 2 Suppose is a continuous random variable with p.d.f. . Find a. b. c. d. Correct! Correct! By LOTUS, By LOTUS, 1 / 1 pts Question 18 Week 2 Module 2 Lesson 7 Question 3 The abbreviation "m.g.f." stands for...

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2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 16 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 a. Mom's generating function b. Mega-gigundo function c. Most-glorious function d. Moment generating function Correct! Correct! 1 / 1 pts Question 19 Week 2 Module 2 Lesson 8 Question 1 Suppose is the result of a 4-sided die toss having sides numbered . Find the probability mass function of . a. Correct! Correct! This follows because b. c. d.

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 17 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 This follows because 1 / 1 pts Question 20 Week 2 Module 2 Lesson 8 Question 2 Suppose ࠵? is a continuous random variable with p.d.f. . Find the p.d.f. of . a. b. c. d. Correct! Correct!

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 18 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 First of all, the c.d.f. of Y is where the range of follows since and . Thus, the p.d.f. of is , for First of all, the c.d.f. of Y is where the range of follows since and . Thus, the p.d.f. of is , for 1 / 1 pts Question 21 Week 2 Module 2 Lesson 9 Question 1

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2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 19 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 The following table gives the joint p.m.f. of two random variables (the GPA of a University of Georgia student) and (his IQ). What's the probability that a random UGA student has an IQ of ? a. b. c. Correct! Correct! Here is the same table with the marginal information filled in: You can see from the table that . Or, you can do it directly via d.

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 20 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 Here is the same table with the marginal information filled in: You can see from the table that . Or, you can do it directly via 1 / 1 pts Question 22 Week 2 Module 2 Lesson 9 Question 2 YES or NO? Suppose and have joint p.d.f. and . Are and independent? a. Yes Correct! Correct! The lesson has a theorem that says that if with no funny limits for some functions and , then are independent. Just choose, for instance, , and note that we don't have funny limits. Then we are done. b. No

2024/1/28, 11 : 50 Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY Page 21 of 21 https://gatech.instructure.com/courses/360616/quizzes/510395 ? module_item_id=3598378 The lesson has a theorem that says that if with no funny limits for some functions and , then are independent. Just choose, for instance, , and note that we don't have funny limits. Then we are done.

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