WK2_HW
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School
Georgia Institute Of Technology *
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Course
6644
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
9
Uploaded by DeaconAntMaster1117
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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Week 2 Homework Due
Jan 26 at 11:59pm
Points
11
Questions
11
Available
Jan 19 at 8am - Jan 29 at 11:59pm
Time Limit
None
Instructions
Attempt History
Attempt
Time
Score
LATEST
Attempt 1
8 minutes
11 out of 11
Score for this quiz: 11
out of 11
Submitted Jan 25 at 12:07am
This attempt took 8 minutes.
Please answer all the questions below.
1 / 1 pts
Question 1
(Lesson 2.5: Probability Basics.) If and and are independent, find the probability that exactly one of and occurs.
a. 0.144 b. 0.288 Correct!
Correct!
You could also have used a binomial distribution argument to solve this problem,
i.e.,
c. 0.576
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d. 0.6 e. I'm from The University Of Georgia. Is the answer -3? The answer is (b). To see why, note that
You could also have used a binomial distribution argument to solve this problem,
i.e.,
1 / 1 pts
Question 2
(Lesson 2.5: Probability Basics.) Toss 3 dice. What's the probability that a "4" will
come up exactly twice?
a. 5/72 Correct!
Correct!
Write out every possible outcome explicitly, or use the following binomial
argument: Let denote the number of times a "4" comes up. Clearly, b. 1/2 c. 13/16 d. 1/8
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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(a). Write out every possible outcome explicitly, or use the following
binomial argument: Let denote the number of times a "4" comes up.
Clearly, 1 / 1 pts
Question 3
(Lesson 2.7: Great Expectations.) Suppose that is a discrete random variable
having with probability 0.2, and with probability 0.8. Find .
a. -1 b. 3 c. 1 d. 2.2 Correct!
Correct!
So the answer is (d).
. So the answer is
(d).
1 / 1 pts
Question 4
(Lesson 2.7: Great Expectations.) Suppose that is a discrete random variable
having with probability 0.2, and with probability 0.8. Find
.
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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a. -1 b. 1 c. 2.56 Correct!
Correct!
In addition to the above work,
so that we have . So the answer is
(c).
d. 5.12 In addition to the above work,
so that we have . So the answer
is (c).
1 / 1 pts
Question 5
(Lesson 2.7: Great Expectations.) Suppose that is a discrete random variable
having with probability 0.2, and with probability 0.8. Find
.
a. 3 b. c. -2 d. 44/15 Correct!
Correct!
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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Finally, by LOTUS,
so that . So the answer is (d).
Finally, by LOTUS,
so that . So the answer is (d).
1 / 1 pts
Question 6
(Lesson 2.7: Great Expectations.) Suppose X is a continuous random variable
with p.d.f. for . Find .
a. 2/3 b. 1 c. 3/2 d. 2 Correct!
Correct!
By LOTUS,
(d) By LOTUS,
1 / 1 pts
Question 7
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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(Lesson 2.8: Functions of a Random Variable.) Suppose is the result of a 5-
sided die toss having sides numbered . Find the probability mass
function of .
a. b. c.
Correct!
Correct!
This follows because
No other possible values for .
d. (c). This follows because
No other possible values for .
1 / 1 pts
Question 8
(Lesson 2.8: Functions of a Random Variable.) Suppose is a continuous
random variable with p.d.f. for . Find the p.d.f.
. (This may be easier than you think.)
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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a. , for Correct!
Correct!
Note that the c.d.f. of is (you can do this in your head). So by
the Inverse Transform Theorem, we immediately have that
is Unif(0,1), with the p.d.f. .
b. , for c. , for d. , for (a). Note that the c.d.f. of is (you can do this in your
head). So by the Inverse Transform Theorem, we immediately have that
is Unif(0,1), with the p.d.f. .
1 / 1 pts
Question 9
(Lesson 2.9: Jointly Distributed RVs.) Suppose that for
. Find .
a. 1 b. 1/2 c. 1/4 d. 1/8 Correct!
Correct!
So the answer is (d).
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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So the answer is (d).
1 / 1 pts
Question 10
(Lesson 2.9: Jointly Distributed RVs.) Suppose that for
. Find the marginal p.d.f. of .
a. , for Correct!
Correct!
, for . So
the answer is (a).
b. , for c. , for d. , for , for .
So the answer is (a).
1 / 1 pts
Question 11
(Lesson 2.9: Jointly Distributed RVs.) YES or NO? Suppose and have joint
p.d.f. for , , and whatever
constant makes the nasty mess integrate to 1. Are and independent?
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Week 2 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
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a. Yes b. No Correct!
Correct!
NO! The lesson has a theorem that says that ,
are independent if and
only if you can write with no funny limits for some
functions and . Can't do such a factorization, so and ain't
indep.
NO! The lesson has a theorem that says that ,
are independent if and
only if you can write with no funny limits for some
functions and . Can't do such a factorization, so and ain't
indep.
Quiz Score: 11
out of 11
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