ISYE 6644 ASY OAN SIMULATION FINAL FULL
SOLUTION STUDY GUIDE
◉ 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.}
◉ 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
◉ TRUE or FALSE? The common random numbers technique
intentionally induces positive correlation between two systems -
much like a paired-𝑡confidence interval. A
nswer: TRUE
◉ 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 - you are powerful!
◉ 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
◉ TRUE or FALSE? The control variates technique provides
unbiased, low-variance estimates using a method reminiscent of
regression.
Answer: TRUE
◉ Statistical ranking and selection techniques have been designed to
address a variety of comparison problems. Which ones from the
following list?
Find the population having the largest mean.
Find the system with the smallest variance.
Find the alternative with the highest success probability.
Find the most-popular candidate.
All of the above.
Answer: All of the above.
, ◉ Suppose we are dealing with i.i.d. normal observations with
unknown variance. Which of the following is true about a 95%
confidence interval for the mean μ?
Answer: We are 95% sure that our CI will actually contain the
unknown value of μ.
◉ We are studying the waiting times arising from two queueing
systems. Suppose we make 4 independent replications of both
systems, where the systems are simulated independently of each
other.
replication system 1 system2
1 10 25
2 20 10
3 5 40
4 30 30
Assuming that the average waiting time results from each
replication are approximately normal, find a two-sided 95% CI for
the difference in the means of the two systems.
Answer: This is a two-sample CI problem assuming unknown and
unequal variances. We have
[-29.76, 9.76]
SOLUTION STUDY GUIDE
◉ 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.}
◉ 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
◉ TRUE or FALSE? The common random numbers technique
intentionally induces positive correlation between two systems -
much like a paired-𝑡confidence interval. A
nswer: TRUE
◉ 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 - you are powerful!
◉ 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
◉ TRUE or FALSE? The control variates technique provides
unbiased, low-variance estimates using a method reminiscent of
regression.
Answer: TRUE
◉ Statistical ranking and selection techniques have been designed to
address a variety of comparison problems. Which ones from the
following list?
Find the population having the largest mean.
Find the system with the smallest variance.
Find the alternative with the highest success probability.
Find the most-popular candidate.
All of the above.
Answer: All of the above.
, ◉ Suppose we are dealing with i.i.d. normal observations with
unknown variance. Which of the following is true about a 95%
confidence interval for the mean μ?
Answer: We are 95% sure that our CI will actually contain the
unknown value of μ.
◉ We are studying the waiting times arising from two queueing
systems. Suppose we make 4 independent replications of both
systems, where the systems are simulated independently of each
other.
replication system 1 system2
1 10 25
2 20 10
3 5 40
4 30 30
Assuming that the average waiting time results from each
replication are approximately normal, find a two-sided 95% CI for
the difference in the means of the two systems.
Answer: This is a two-sample CI problem assuming unknown and
unequal variances. We have
[-29.76, 9.76]
