Week 3 Homework_ Simulation - ISYE-6644-OAN_O01_Q_ASY
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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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Week 3 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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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?
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