Week 10 Homework
Due Mar 29 at 11:59pm Points 9 Questions 10
Available after Mar 13 at 8am Time Limit None
Aħempt History
Attempt Time Score
LATEST Attempt 1 22,313 minutes 5 out of 9
Score for this quiz: 5 out of
...
Week 10 Homework
Due Mar 29 at 11:59pm Points 9 Questions 10
Available after Mar 13 at 8am Time Limit None
Aħempt History
Attempt Time Score
LATEST Attempt 1 22,313 minutes 5 out of 9
Score for this quiz: 5 out of 9
Submitted Mar 29 at 11:59pm
This attempt took 22,313 minutes.
Question 1 0 / 1 pts
(Lesson 7.11: Composition.) BONUS: It's Raining Cats and Dogs is a pet
store with 60% cats and 40% dogs. The weights of cats are Nor(12,4),
and the weights of dogs are Nor(30,25). How would we use composition
to simulate the weight of a random pet from the store? (Let
denote the standard normal c.d.f., and let 's denote PRN's.)
a.
b.
c. If , then ; otherwise,
ou Answered ou Answered
d. If , then ; otherwise,
orrect Answer orrect Answer4/15/2020 Week 10 Homework: Simulation - ISYE-6644-OAN/O01
e. If , then ; otherwise,
By inverse transform, the weight of a cat all by itself is
Similarly, the weight of a dog all by itself is .
These facts eliminate choices (a), (c), and (e). In addition, (a) and
(b) are some kind of mutant cat-dog, both of which sort of combine
0.6 of a cat with 0.4 of a dog; so those are wrong. What we really
want is to take with probability 0.6, and otherwise
. This is choice (d)!
Question 2 1 / 1 pts
(Lesson 7.12: The Box-Muller Method.) Suppose and are i.i.d.
Unif(0,1) with and . Use the "cosine" version of BoxMuller to generate a single Nor(-1,4) random variate. Don't forget to use
radians instead of degrees!
a. -0.326
b. 0
Correct! Correct! c. 0.326
d. 0.663
e. 1.964/15/2020 Week 10 Homework: Simulation - ISYE-6644-OAN/O01
https://gatech.instructure.com/courses/106512/quizzes/96333?module_item_id=530696 3/10
Box-Muller immediately gives the following Nor(0,1) random
variate:
To obtain the realization of the Nor($-$1,4), we simply apply the
transform
which is choice (c).
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