9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
Week 1 Homework
Due Sep 4 at 11:59pm
Points 12
Questions 12
Available Aug 28 at 8am - Sep 7 at 11:59pm
Time Limit None
Instructions
Please answer all the questions below.
This quiz was locked Sep 7 at 11:59pm.
Attempt History
Attempt Time Score
LATEST Attempt 1 827 minutes 12 out of 12
Score for this quiz: 12 out of 12
Submitted Aug 29 at 6:13pm
This attempt took 827 minutes.
Correct answer
Question 1
pts
(Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having height = 1000 feet.
You're a strong bloke, so the initial downward velocity is = -100 feet/sec (slightly under 70 miles/hr).
Further, in this neck of the woods, it turns out there is no friction in the atmosphere - amazing! Now you
remember from your Baby Physics class that the height after time is
When does the rock hit the ground?
a. -11.625 sec
b. 2 sec
c. 5.375 sec
Set
and solve for t. Quadratics are easy:
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 1/9
,9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
which we take as the answer since the negative answer doesn't make practical sense.
d. 11.625 sec
e. 10 sec
Set
and solve for t. Quadratics are easy:
which we take as the answer since the negative answer doesn't make practical sense.
Correct answer
Question 2
pts
(Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between
customer arrivals are independent, identically distributed Exp(λ = 2/hr) random variables; and the service
times are i.i.d. Exp(µ = 3/hr). Unfortunately, if a potential arriving customer sees that the server is
occupied, he gets mad and leaves the system. Thus, the system can have either 0 or 1 customer in it at
any time. This is what’s known as an M/M/1/1 queue. If denotes the probability that a customer is
being served at time t, trust me that it can be shown that
If the system is empty at time 0, i.e., , what is the probability that there will be no people in the
system at time 1 hr?
a. 1
b. 2/3
c. 0.397
d. 0.603
At time , we have
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,9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
At time , we have
Correct answer
Question 3
pts
(Lesson 1.4: History.) Harry Markowitz (one of the big wheels in simulation language development) won
his Nobel Prize for portfolio theory in 1990, though the work that earned him the award was conducted
much earlier in the 1950s. Who won the 1990 Prize with him? You are allowed to look this one up.
a. Merton Miller and William Sharpe
for accomplishments in related (but slightly different) subject areas.
b. Henry Kissinger
c. Albert Einstein
d. Subrahmanyan Chandrasekhar
for accomplishments in related (but slightly different) subject areas.
Correct answer
Question 4
pts
(Lesson 1.5: Applications.) Which of the following situations might be good candidates to use simulation?
(There may be more than one correct answer.)
a. We put $5000 into a savings account paying 2% continuously compounded interest per year, and we are interested
in determining the account's value in 5 years.
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 3/9
, 9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
b. We are interested in investing one half of our portfolio in fixed-interest U.S. bonds and the remaining half in a stock
market equity index. We have some information concerning the distribution of stock market returns, but we do not really
know what will happen in the market with certainty.
c. We have a new strategy for baseball batting orders, and we would like to know if this strategy beats other commonly
used batting orders (e.g., a fast guy bats first, a big, strong guy bats fourth, etc.). We have information on the
performance of the various team members, but there’s a lot of randomness in baseball.
d. We have an assembly station in which “customers” (for instance, parts to be manufactured) arrive every 5 minutes
exactly and are processed in precisely 4 minutes by a single server. We would like to know how many parts the server
can produce in a hour.
e. Consider an assembly station in which parts arrive randomly, with independent exponential interarrival times. There is
a single server who can process the parts in a random amount of time that is normally distributed. Moreover, the server
takes random breaks every once in a while. We would like to know how big any line is likely to get.
f. Suppose we are interested in determining the number of doctors needed on Friday night at a local emergency room.
We need to ensure that 90% of patients get treatment within one hour.
(a) and (d) do not require simulation, since we can easily “solve” those models with a simple equation or
two. (b), (c), (e), and (f) will likely require simulation.
Correct answer
Question 5
pts
(Lessons 1.6 and 1.7: Baby Examples.) The planet Glubnor has 50-day years.
Suppose there are 2 Glubnorians in the room. What’s the probability that they’ll have the same birthday?
a. 1/(49 · 50)
b. 1/50
b. Let’s call the two guys A and B. Whatever A’s birthday is, the probability that B matches it is 1/50.
Let’s try it another way. The total number of ways that two people can have birthdays is 50 × 50 = 2500.
The total number of ways that they can have two different birthdays is 50 × 49 = 2450. Thus,
c. 1/25
d. 2/49
Let’s call the two guys A and B. Whatever A’s birthday is, the probability that B matches it is 1/50.
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 4/9
Week 1 Homework
Due Sep 4 at 11:59pm
Points 12
Questions 12
Available Aug 28 at 8am - Sep 7 at 11:59pm
Time Limit None
Instructions
Please answer all the questions below.
This quiz was locked Sep 7 at 11:59pm.
Attempt History
Attempt Time Score
LATEST Attempt 1 827 minutes 12 out of 12
Score for this quiz: 12 out of 12
Submitted Aug 29 at 6:13pm
This attempt took 827 minutes.
Correct answer
Question 1
pts
(Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having height = 1000 feet.
You're a strong bloke, so the initial downward velocity is = -100 feet/sec (slightly under 70 miles/hr).
Further, in this neck of the woods, it turns out there is no friction in the atmosphere - amazing! Now you
remember from your Baby Physics class that the height after time is
When does the rock hit the ground?
a. -11.625 sec
b. 2 sec
c. 5.375 sec
Set
and solve for t. Quadratics are easy:
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 1/9
,9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
which we take as the answer since the negative answer doesn't make practical sense.
d. 11.625 sec
e. 10 sec
Set
and solve for t. Quadratics are easy:
which we take as the answer since the negative answer doesn't make practical sense.
Correct answer
Question 2
pts
(Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between
customer arrivals are independent, identically distributed Exp(λ = 2/hr) random variables; and the service
times are i.i.d. Exp(µ = 3/hr). Unfortunately, if a potential arriving customer sees that the server is
occupied, he gets mad and leaves the system. Thus, the system can have either 0 or 1 customer in it at
any time. This is what’s known as an M/M/1/1 queue. If denotes the probability that a customer is
being served at time t, trust me that it can be shown that
If the system is empty at time 0, i.e., , what is the probability that there will be no people in the
system at time 1 hr?
a. 1
b. 2/3
c. 0.397
d. 0.603
At time , we have
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 2/9
,9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
At time , we have
Correct answer
Question 3
pts
(Lesson 1.4: History.) Harry Markowitz (one of the big wheels in simulation language development) won
his Nobel Prize for portfolio theory in 1990, though the work that earned him the award was conducted
much earlier in the 1950s. Who won the 1990 Prize with him? You are allowed to look this one up.
a. Merton Miller and William Sharpe
for accomplishments in related (but slightly different) subject areas.
b. Henry Kissinger
c. Albert Einstein
d. Subrahmanyan Chandrasekhar
for accomplishments in related (but slightly different) subject areas.
Correct answer
Question 4
pts
(Lesson 1.5: Applications.) Which of the following situations might be good candidates to use simulation?
(There may be more than one correct answer.)
a. We put $5000 into a savings account paying 2% continuously compounded interest per year, and we are interested
in determining the account's value in 5 years.
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 3/9
, 9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
b. We are interested in investing one half of our portfolio in fixed-interest U.S. bonds and the remaining half in a stock
market equity index. We have some information concerning the distribution of stock market returns, but we do not really
know what will happen in the market with certainty.
c. We have a new strategy for baseball batting orders, and we would like to know if this strategy beats other commonly
used batting orders (e.g., a fast guy bats first, a big, strong guy bats fourth, etc.). We have information on the
performance of the various team members, but there’s a lot of randomness in baseball.
d. We have an assembly station in which “customers” (for instance, parts to be manufactured) arrive every 5 minutes
exactly and are processed in precisely 4 minutes by a single server. We would like to know how many parts the server
can produce in a hour.
e. Consider an assembly station in which parts arrive randomly, with independent exponential interarrival times. There is
a single server who can process the parts in a random amount of time that is normally distributed. Moreover, the server
takes random breaks every once in a while. We would like to know how big any line is likely to get.
f. Suppose we are interested in determining the number of doctors needed on Friday night at a local emergency room.
We need to ensure that 90% of patients get treatment within one hour.
(a) and (d) do not require simulation, since we can easily “solve” those models with a simple equation or
two. (b), (c), (e), and (f) will likely require simulation.
Correct answer
Question 5
pts
(Lessons 1.6 and 1.7: Baby Examples.) The planet Glubnor has 50-day years.
Suppose there are 2 Glubnorians in the room. What’s the probability that they’ll have the same birthday?
a. 1/(49 · 50)
b. 1/50
b. Let’s call the two guys A and B. Whatever A’s birthday is, the probability that B matches it is 1/50.
Let’s try it another way. The total number of ways that two people can have birthdays is 50 × 50 = 2500.
The total number of ways that they can have two different birthdays is 50 × 49 = 2450. Thus,
c. 1/25
d. 2/49
Let’s call the two guys A and B. Whatever A’s birthday is, the probability that B matches it is 1/50.
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 4/9
