ISYE 6644 final | Questions and Answers |
Verified A+ Pack
• 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. -✓✓True
• 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. -✓✓True
• For which scenarios(s) below might it be appropriate to use a Bernoulli selection
procedure?
a) Find the inventory policy having the largest profit.
b) Find the drug giving the best chance of a cure.
c) Find the maintenance policy having the lowest failure probability.
d) Find the scheduling rule that that has the best chance of making an on-time delivery.
-✓✓All three of (b), (c), and (d).
• Suppose that a Bernoulli selection procedure tells you to take 100 observations from
each of two populations, A and B. It turns out that A gets 85 successes and B gets 46
successes. What do you think? -✓✓1) A almost certainly has a higher success
probability than B.
2) We could've probably stopped sampling a bit earlier (i.e., with fewer than 100
observations) because A was so far ahead of B.
• For which scenarios(s) below might it be appropriate to use a multinomial selection
procedure? -✓✓Find the most-popular political candidate.
• 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 ration of the highest-to-second-highest preference probabilities
happens to be at least 0*=1.4. How many people does the single-stage procedure
Mbem require us to interview? -✓✓126
Go to the table in the notes and pick off the entry for k=3, P^⋆=0.90, and θ^⋆=1.4.
• Which of the following parameters can you get confidence intervals for?
Means
Variances
Quantiles
Differences between the means of two systems -✓✓All of the above
, • If we have an iid normal sample of observations, X1, X2,...Xn, what probability
distribution is most-commonly used to obtain cofidence intervals for the mean? -✓✓t
• 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. -✓✓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. -
✓✓TRUE
• TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-𝑡confidence interval. -
✓✓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?? -✓✓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. -✓✓TRUE
• TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression. -✓✓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. -✓✓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? -✓✓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
Verified A+ Pack
• 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. -✓✓True
• 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. -✓✓True
• For which scenarios(s) below might it be appropriate to use a Bernoulli selection
procedure?
a) Find the inventory policy having the largest profit.
b) Find the drug giving the best chance of a cure.
c) Find the maintenance policy having the lowest failure probability.
d) Find the scheduling rule that that has the best chance of making an on-time delivery.
-✓✓All three of (b), (c), and (d).
• Suppose that a Bernoulli selection procedure tells you to take 100 observations from
each of two populations, A and B. It turns out that A gets 85 successes and B gets 46
successes. What do you think? -✓✓1) A almost certainly has a higher success
probability than B.
2) We could've probably stopped sampling a bit earlier (i.e., with fewer than 100
observations) because A was so far ahead of B.
• For which scenarios(s) below might it be appropriate to use a multinomial selection
procedure? -✓✓Find the most-popular political candidate.
• 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 ration of the highest-to-second-highest preference probabilities
happens to be at least 0*=1.4. How many people does the single-stage procedure
Mbem require us to interview? -✓✓126
Go to the table in the notes and pick off the entry for k=3, P^⋆=0.90, and θ^⋆=1.4.
• Which of the following parameters can you get confidence intervals for?
Means
Variances
Quantiles
Differences between the means of two systems -✓✓All of the above
, • If we have an iid normal sample of observations, X1, X2,...Xn, what probability
distribution is most-commonly used to obtain cofidence intervals for the mean? -✓✓t
• 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. -✓✓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. -
✓✓TRUE
• TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-𝑡confidence interval. -
✓✓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?? -✓✓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. -✓✓TRUE
• TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression. -✓✓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. -✓✓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? -✓✓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
