Week 8 Module 6 Knowledge Checks (Fall_Spring)_ Simulation - ISYE-6644-OAN_O01_Q_ASY
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Georgia Institute Of Technology *
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Course
6644
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
6
Uploaded by PresidentAnteaterMaster735
3/22/24, 4:05 PM
Week 8 Module 6 Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY
https://gatech.instructure.com/courses/360616/quizzes/510413?module_item_id=3598440
1/6
Week 8 Module 6 Knowledge Checks (Fall/Spring) Due No due date
Points 12
Questions 12
Time Limit None
Allowed Attempts Unlimited
Attempt History
Attempt
Time
Score
KEPT
Attempt 2
5 minutes
12 out of 12
LATEST
Attempt 2
5 minutes
12 out of 12
Attempt 1
29 minutes
11 out of 12
Submitted Mar 3 at 5:33pm
Question 1
1 / 1 pts
a. The numbers must appear to be Unif(0,1).
b. The numbers be approximately independent.
c. We should be able to generate the PRNs very, very quickly.
Correct!
d. We must be able to look up the series of PRNs from a table.
e. We can reproduce any sequence of PRNs if called upon to do so.
Believe it or not, (e) is actually a necessity - we should be able to repeat any experiment if our boss asks
us to!
Question 2
1 / 1 pts
Take the Quiz Again
Week 8 Module 6 Lesson 1 Question 1
Which property is not desirable for a good pseudo-random number generator?
Week 8 Module 6 Lesson 2 Question 1
3/22/24, 4:05 PM
Week 8 Module 6 Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY
https://gatech.instructure.com/courses/360616/quizzes/510413?module_item_id=3598440
2/6
a. Generators involving physical devices such as coin flips or least significant digit readings from an atomic clock.
b. Random number tables.
c. von Neumann's mid-square method.
d. Fibonacci and additive congruential generators.
Correct!
e. All of the above.
Question 3
1 / 1 pts
a. 0
b. 3
c. 2
Correct!
d. 5
e. 18
Note that
Thus,
So the answer is (d).
Question 4
1 / 1 pts
Which of the following PRN generators aren't very good?
Week 8 Module 6 Lesson 3 Question 1
Consider the generator , and suppose that the sequence is initialized with
. Find .
Week 8 Module 6 Lesson 3 Question 2
Again consider the generator , initialized with . Find .
3/22/24, 4:05 PM
Week 8 Module 6 Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY
https://gatech.instructure.com/courses/360616/quizzes/510413?module_item_id=3598440
3/6
a. 0
Correct!
b. 3
c. 2
d. 5
e. 18
According to the class notes (or via a bit of tedious algebra), we know that this is a full-period generator
with a cycle length of . Therefore, . So the answer is (b)
Question 5
1 / 1 pts
Correct!
True
False
We have
;
so the answer is TRUE.
Question 6
1 / 1 pts
a. 27
b. 0
c. 16/32
Correct!
d. 27/32
e. 31/32
Week 8 Module 6 Lesson 4 Question 1
TRUE or FALSE? .
Week 8 Module 6 Lesson 4 Question 2
Consider a Tausworthe generator that produces the bits 1,1,0,1,1. Calculate the resulting pseudo-
random number obtained by transforming these 5 bits from base 2 to base 10, i.e., , where
denotes a number in base 2, e.g. .
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3/22/24, 4:05 PM
Week 8 Module 6 Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY
https://gatech.instructure.com/courses/360616/quizzes/510413?module_item_id=3598440
4/6
, so the answer is (d).
Question 7
1 / 1 pts
Correct!
True
False
TRUE. In fact, the L'Ecuyer generator that we discussed has a period of around , and the Mersenne
Twister chimes in at . Amazing!
Question 8
1 / 1 pts
True
Correct!
False
Really FALSE! RANDU has severe problems with hyperplanes. For instance, recall the pretty 3-D picture
in which you see 15 hyperplanes - they may look cool, but this indicates that the uniform generator
doesn't fill up the space uniformly!
Question 9
1 / 1 pts
Correct!
True
False
Week 8 Module 6 Lesson 5 Question 1
TRUE or FALSE? There are good PRN generators out there having incredible cycle lengths of over .
Week 8 Module 6 Lesson 6 Question 1
TRUE or FALSE? RANDU is a pretty good generator.
Week 8 Module 6 Lesson 7 Question 1
TRUE or FALSE? is the probability of a Type I error.
3/22/24, 4:05 PM
Week 8 Module 6 Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY
https://gatech.instructure.com/courses/360616/quizzes/510413?module_item_id=3598440
5/6
Question 10
1 / 1 pts
a. Goodness-of-fit tests
b. Independence tests.
c. Neither (a) nor (b).
Correct!
d. Both (a) and (b).
Question 11
1 / 1 pts
Correct!
a. Reject the goodness-of-fit test and declare that the PRNs are probably not uniform.
b. Reject the goodness-of-fit test and declare that the PRNs are probably not independent.
c. Accept the goodness-of-fit test and declare that the PRNs are probably uniform.
d. Accept the goodness-of-fit test and declare that the PRNs are probably independent.
e. Panic at the disco!
Question 12
1 / 1 pts
a. 1
b. 2
Correct!
c. 4
Week 8 Module 6 Lesson 7 Question 2
In the context of evaluating a PRN generator, which kinds of statistical tests are we interested in?
Week 8 Module 6 Lesson 8 Question 1
If the goodness-of-fit statistic, , is much greater than the relevant quantile , what do we do?
Week 8 Module 6 Lesson 9 Question 1
Consider the following sequence of pseudo-random numbers.
0.15 0.85 0.23 0.36 0.42 0.49 0.66 0.70 0.81 0.89 0.97 0.85
How many runs "up and down" are there?
3/22/24, 4:05 PM
Week 8 Module 6 Knowledge Checks (Fall/Spring): Simulation - ISYE-6644-OAN/O01/Q/ASY
https://gatech.instructure.com/courses/360616/quizzes/510413?module_item_id=3598440
6/6
d. 11
e. 12
Here is what the runs resulting from the 12 PRNs look like:
+ - + + + + + + + + -
Thus, there are 4 runs, so the answer is (c).
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