Week 2 Knowledge Checks: ISYE-6644 Lesson Insights and Practice

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 2/14  Question 2 1 / 1 pts a. Correct! b. By the chain rule, . c. d. e. I'm from UGA - I'm scared of math, and I don't know! By the chain rule, .  Question 3 1 / 1 pts a. trial-and-error b. bisection c. Newton's method Correct! d. Newman's method acting  Optional: Week 2 Module 2 Lesson 1 Question 2 If , find the derivative 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?

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 3/14 Question 4 1 / 1 pts a. Correct! b. 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 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.) Optional: Week 2 Module 2 Lesson 2 Question 2 BONUS. Use your favorite numerical method to solve

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 4/14 After a few more iterations, and you’ll indeed see that this thing appears to be converging to ...  Question 5 1 / 1 pts a. b. c. Correct! d. We have We have  Question 6 1 / 1 pts Optional: Week 2 Module 2 Lesson 3 Question 1 Find . Optional: Week 2 Module 2 Lesson 3 Question 2

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3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 5/14 a. Correct! b. This is tricky. You have to use integration by parts with and (using the notation of the notes). Then c. d. This is tricky. You have to use integration by parts with and (using the notation of the notes). Then  Question 7 1 / 1 pts BONUS. Find Optional: Week 2 Module 2 Lesson 3 Question 3

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 6/14 Correct! a. 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):  Question 8 1 / 1 pts a. Riemann sums Correct! b. Newmann sums Never heard of it! c. Trapezoid Rule d. The Monte Carlo method Never heard of it!  Question 9 0.5 / 1 pts BONUS. Find . (Hint: this problem will make you so sick, you'll have to go to the...? ) Optional: Week 2 Module 2 Lesson 4 Question 1 Which of the following is not an integration method discussed in this lesson? Optional: Week 2 Module 2 Lesson 4 Question 2

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 7/14 a. You catch a zoid b. You capture a zoid Correct Answer c. You trap a zoid Correct! d. Trick question! It's always best to avoid a zoid altogether!  Question 10 1 / 1 pts a. Correct! b. 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.  How does a mathematician capture a wild man-eating zoid? Select all that apply. Optional: Week 2 Module 2 Lesson 4 Question 3 Find the approximate value of the integral using the lesson's form of the Riemann sum with , specifically,

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3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 8/14 Question 11 1 / 1 pts a. b. c. Correct! d. Each of has probability of turning up on a particular toss. Thus, Each of has probability of turning up on a particular toss. Thus,  Question 12 0 / 1 pts You Answered True Correct Answer False In order to be a legit p.d.f., must integrate to 1; but lo and behold. . .  Week 2 Module 2 Lesson 5 Question 1 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 ? Week 2 Module 2 Lesson 5 Question 2 TRUE or FALSE? is a legitimate probability density function. f(x) ☹

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 9/14 Question 13 1 / 1 pts a. Normal Correct! b. Unif (0,1) This is simply the amazing Inverse Transform Theorem. c. Exponential d. Weibull This is simply the amazing Inverse Transform Theorem.  Question 14 0 / 1 pts a. Normal You Answered b. Unif (0,1) Correct Answer c. Exponential d. Weibull This is a consequence of the Inverse Transform Theorem.  Question 15 1 / 1 pts 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 ? Week 2 Module 2 Lesson 6 Question 2 Suppose is a Unif (0,1) random variable. Name the distribution of Week 2 Module 2 Lesson 6 Question 3

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 10/14 Correct! True 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.  Question 16 1 / 1 pts a. Correct! b. c. d.  Question 17 0 / 1 pts You Answered a. b. c. BONUS: TRUE or FALSE? is a prime number.. Week 2 Module 2 Lesson 7 Question 1 Suppose is a continuous random variable with p.d.f. Find Week 2 Module 2 Lesson 7 Question 2 Suppose is a continuous random variable with p.d.f. . Find

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3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 11/14 Correct Answer d. By LOTUS,  Question 18 1 / 1 pts a. Mom's generating function b. Mega-gigundo function c. Most-glorious function Correct! d. Moment generating function  Question 19 1 / 1 pts Correct! a. This follows because b. Week 2 Module 2 Lesson 7 Question 3 The abbreviation "m.g.f." stands for... 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 .

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 12/14 c. d. This follows because  Question 20 0 / 1 pts a. You Answered b. c. Correct Answer d. First of all, the c.d.f. of is where the range of follows since and . Thus, the p.d.f. of is , for  Week 2 Module 2 Lesson 8 Question 2 Suppose 𝑋 is a continuous random variable with p.d.f. . Find the p.d.f. of . Y

3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 13/14 Question 21 1 / 1 pts a. b. Correct! c. 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. 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  Week 2 Module 2 Lesson 9 Question 1 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 ?

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3/14/24, 11:13 PM Week 2 Module 2 (L1-9) Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY https://gatech.instructure.com/courses/360616/quizzes/510395?module_item_id=3598378 14/14 Question 22 1 / 1 pts Correct! a. Yes 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 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. Week 2 Module 2 Lesson 9 Question 2 YES or NO? Suppose and have joint p.d.f. and . Are and independent?

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