ISYE-6644 SIMULATION EXAM
QUESTIONS WITH COMPLETE
SOLUTIONS
(10.4) TRUE or FALSE? The paired CI for the differences in two means is designed to
work especially well if all of the observations from the first population are completely
independent of all of the observations from the second population. - Answer-FALSE. {In
fact, it's easier to distinguish between the two means if Xi is positively correlated with Yi.
Think about my parallel parking example in the class notes.}
(10.5) TRUE or FALSE? You can use a version of independent replications to obtain
confidence intervals for the difference in the means from two simulation models.` -
Answer-TRUE. {It's pretty straightforward, though the notation is a little more tedious}.
(10.6) TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-t confidence interval. -
Answer-True
(10.6) CRN depends on someone's ability to manipulate the underlying pseudo-random
numbers - e.g., use the same arrival times when simulating two competing simulated
systems. So who ultimately controls those PRNs?? - Answer-You do
Anithetic Random Numbers Method - Answer-Used for negative correlation between
estimators. Opposite of CRN
CRN - Answer-Common Random Numbers
(10.7) TRUE or FALSE? The antithetic random numbers technique intentionally induces
negative correlation between two runs of the same system - this allows us to better
estimate the mean of the system. - Answer-True
(10.8) TRUE or FALSE? The control variates technique provides unbiased, low-
variance estimates using a method reminiscent of regression. - Answer-True
(10.9) Statistical ranking and selection techniques have been designed to address a
variety of comparison problems. Which ones from the following list? (a) Find the
population having the largest mean.
(b) Find the system with the smallest variance.
(c) Find the alternative with the highest success probability.
(d) Find the most-popular candidate. - Answer-All of them
, (10.10) What is a possible goal of an indifference-zone normal means selection
technique? - Answer-Find the normal population having the largest mean, especially if
the largest mean is ≫ the second-largest. Using the notation of the notes, we want to
make sure to get the right answer in the case that μk − μk−1 ≥ δ⋆.
(10.11) TRUE or FALSE? The Bechhofer procedure for selecting the normal population
with the largest mean specifies the appropriate number of observations to take from
each competing population, and simply selects the competitor having the largest sample
mean. - Answer-True
(10.12) TRUE or FALSE? Sometimes a single-stage procedure like Bechhofer's is
inefficient. In fact, it's possible to use certain sequential procedures that take
observations one-at-a-time (instead of all at once in a single stage) to make good
selection decisions using fewer observations. - Answer-True
(10.16) Suppose that we want to know which of Coke, Pepsi, and Dr. Pepper is the
most popular. We would like to make the correct selection with probability of at least
P⋆=0.90 in the event that the ratio of the highest-to-second-highest preference
probabilities happens to be at least θ⋆=1.4. How many people does the single-stage
procedure M{BEM} require us to interview? - Answer-From table, find P* = 0.9, Theta* =
1.4 and k = 3 competitors
(Lesson 9.1: Introduction to Output Analysis.) Which of the following problems might
best be characterized by a finite-horizon simulation?
a. Simulating long-term hurricane patterns
b. Simulating a manufacturing cell 24/7/365
c. Simulating the operations of a bank from 9:00 a.m. until 5:00 p.m.
d. Simulating the steady-state distribution of a Markov chain - Answer-c. Simulating the
operations of a bank from 9:00 a.m. until 5:00 p.m.
(Lesson 9.1: Introduction to Output Analysis.) Let's run a simulation whose output is a
sequence of daily inventory levels for a particular product. Which of the following
statements is true?
a. The consecutive daily inventory levels are independent.
b. The consecutive daily inventory levels are uncorrelated.
c. The consecutive daily inventory levels are normally distributed.
d. The consecutive daily inventory levels may not be identically distributed. - Answer-d.
The consecutive daily inventory levels may not be identically distributed.
(Lesson 8.2: Identifying Distributions.) Let's play Name That Distribution!
The number of times a "3" comes up in 10 dice tosses.
a. Bernoulli
b. Binomial
c. Geometric
d. Negative Binomial
QUESTIONS WITH COMPLETE
SOLUTIONS
(10.4) TRUE or FALSE? The paired CI for the differences in two means is designed to
work especially well if all of the observations from the first population are completely
independent of all of the observations from the second population. - Answer-FALSE. {In
fact, it's easier to distinguish between the two means if Xi is positively correlated with Yi.
Think about my parallel parking example in the class notes.}
(10.5) TRUE or FALSE? You can use a version of independent replications to obtain
confidence intervals for the difference in the means from two simulation models.` -
Answer-TRUE. {It's pretty straightforward, though the notation is a little more tedious}.
(10.6) TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-t confidence interval. -
Answer-True
(10.6) CRN depends on someone's ability to manipulate the underlying pseudo-random
numbers - e.g., use the same arrival times when simulating two competing simulated
systems. So who ultimately controls those PRNs?? - Answer-You do
Anithetic Random Numbers Method - Answer-Used for negative correlation between
estimators. Opposite of CRN
CRN - Answer-Common Random Numbers
(10.7) TRUE or FALSE? The antithetic random numbers technique intentionally induces
negative correlation between two runs of the same system - this allows us to better
estimate the mean of the system. - Answer-True
(10.8) TRUE or FALSE? The control variates technique provides unbiased, low-
variance estimates using a method reminiscent of regression. - Answer-True
(10.9) Statistical ranking and selection techniques have been designed to address a
variety of comparison problems. Which ones from the following list? (a) Find the
population having the largest mean.
(b) Find the system with the smallest variance.
(c) Find the alternative with the highest success probability.
(d) Find the most-popular candidate. - Answer-All of them
, (10.10) What is a possible goal of an indifference-zone normal means selection
technique? - Answer-Find the normal population having the largest mean, especially if
the largest mean is ≫ the second-largest. Using the notation of the notes, we want to
make sure to get the right answer in the case that μk − μk−1 ≥ δ⋆.
(10.11) TRUE or FALSE? The Bechhofer procedure for selecting the normal population
with the largest mean specifies the appropriate number of observations to take from
each competing population, and simply selects the competitor having the largest sample
mean. - Answer-True
(10.12) TRUE or FALSE? Sometimes a single-stage procedure like Bechhofer's is
inefficient. In fact, it's possible to use certain sequential procedures that take
observations one-at-a-time (instead of all at once in a single stage) to make good
selection decisions using fewer observations. - Answer-True
(10.16) Suppose that we want to know which of Coke, Pepsi, and Dr. Pepper is the
most popular. We would like to make the correct selection with probability of at least
P⋆=0.90 in the event that the ratio of the highest-to-second-highest preference
probabilities happens to be at least θ⋆=1.4. How many people does the single-stage
procedure M{BEM} require us to interview? - Answer-From table, find P* = 0.9, Theta* =
1.4 and k = 3 competitors
(Lesson 9.1: Introduction to Output Analysis.) Which of the following problems might
best be characterized by a finite-horizon simulation?
a. Simulating long-term hurricane patterns
b. Simulating a manufacturing cell 24/7/365
c. Simulating the operations of a bank from 9:00 a.m. until 5:00 p.m.
d. Simulating the steady-state distribution of a Markov chain - Answer-c. Simulating the
operations of a bank from 9:00 a.m. until 5:00 p.m.
(Lesson 9.1: Introduction to Output Analysis.) Let's run a simulation whose output is a
sequence of daily inventory levels for a particular product. Which of the following
statements is true?
a. The consecutive daily inventory levels are independent.
b. The consecutive daily inventory levels are uncorrelated.
c. The consecutive daily inventory levels are normally distributed.
d. The consecutive daily inventory levels may not be identically distributed. - Answer-d.
The consecutive daily inventory levels may not be identically distributed.
(Lesson 8.2: Identifying Distributions.) Let's play Name That Distribution!
The number of times a "3" comes up in 10 dice tosses.
a. Bernoulli
b. Binomial
c. Geometric
d. Negative Binomial
