ISYE 6644 - Final prep ACTUAL UPDATED QUESTIONS AND CORRECT
ANSWERS
What is a possible goal of an indifference-zone normal Find the normal population having the largest mean, especially if the largest mean
means selection technique? is ≫ the second-largest.
TRUE or FALSE? The Bechhofer procedure for selecting True
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 or FALSE? Sometimes a single-stage procedure like True
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.
For which scenarios(s) below might it be appropriate to All three of (b), (c), and (d).
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.
Suppose that a Bernoulli selection procedure tells you to 1) A almost certainly has a higher success probability than B.
take 100 observations from each of two populations, A 2) We could've probably stopped sampling a bit earlier (i.e., with fewer than 100
and B. It turns out that A gets 85 successes and B gets 46 observations) because A was so far ahead of B.
successes. What do you think?
For which scenarios(s) below might it be appropriate to Find the most-popular political candidate.
use a multinomial selection procedure?
Suppose that we want to know which of Coke, Pepsi and 126
Dr.pepper is the most popular. We would like to make the Go to the table in the notes and pick off the entry for k=3, P^⋆=0.90, and θ^⋆=1.4.
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?
, Which of the following parameters can you get All of the above
confidence intervals for?
Means
Variances
Quantiles
Differences between the means of two systems
If we have an iid normal sample of observations, X1, t
X2,...Xn, what probability distribution is most-commonly
used to obtain cofidence intervals for the mean?
TRUE or FALSE? The paired CI for the differences in two FALSE. {In fact, it's easier to distinguish between the two means if Xi is positively
means is designed to work especially well if all of the correlated with Yi. Think about my parallel parking example in the class notes.}
observations from the first population are completely
independent of all of the observations from the second
population.
TRUE or FALSE? You can use a version of independent TRUE
replications to obtain confidence intervals for the
difference in the means from two simulation models.
TRUE or FALSE? The common random numbers TRUE
technique intentionally induces positive correlation
between two systems - much like a paired-𝑡confidence
interval.
CRN depends on someone's ability to manipulate the You do - you are powerful!
underlying pseudo-random numbers - e.g., use the same
arrival times when simulating two competing simulated
systems. So who ultimately controls those PRNs??
TRUE or FALSE? The antithetic random numbers TRUE
technique intentionally induces negative correlation
between two runs of the same system - this allows us to
better estimate the mean of the system.
TRUE or FALSE? The control variates technique provides TRUE
unbiased, low-variance estimates using a method
reminiscent of regression.
Statistical ranking and selection techniques have been All of the above.
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.
ANSWERS
What is a possible goal of an indifference-zone normal Find the normal population having the largest mean, especially if the largest mean
means selection technique? is ≫ the second-largest.
TRUE or FALSE? The Bechhofer procedure for selecting True
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 or FALSE? Sometimes a single-stage procedure like True
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.
For which scenarios(s) below might it be appropriate to All three of (b), (c), and (d).
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.
Suppose that a Bernoulli selection procedure tells you to 1) A almost certainly has a higher success probability than B.
take 100 observations from each of two populations, A 2) We could've probably stopped sampling a bit earlier (i.e., with fewer than 100
and B. It turns out that A gets 85 successes and B gets 46 observations) because A was so far ahead of B.
successes. What do you think?
For which scenarios(s) below might it be appropriate to Find the most-popular political candidate.
use a multinomial selection procedure?
Suppose that we want to know which of Coke, Pepsi and 126
Dr.pepper is the most popular. We would like to make the Go to the table in the notes and pick off the entry for k=3, P^⋆=0.90, and θ^⋆=1.4.
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?
, Which of the following parameters can you get All of the above
confidence intervals for?
Means
Variances
Quantiles
Differences between the means of two systems
If we have an iid normal sample of observations, X1, t
X2,...Xn, what probability distribution is most-commonly
used to obtain cofidence intervals for the mean?
TRUE or FALSE? The paired CI for the differences in two FALSE. {In fact, it's easier to distinguish between the two means if Xi is positively
means is designed to work especially well if all of the correlated with Yi. Think about my parallel parking example in the class notes.}
observations from the first population are completely
independent of all of the observations from the second
population.
TRUE or FALSE? You can use a version of independent TRUE
replications to obtain confidence intervals for the
difference in the means from two simulation models.
TRUE or FALSE? The common random numbers TRUE
technique intentionally induces positive correlation
between two systems - much like a paired-𝑡confidence
interval.
CRN depends on someone's ability to manipulate the You do - you are powerful!
underlying pseudo-random numbers - e.g., use the same
arrival times when simulating two competing simulated
systems. So who ultimately controls those PRNs??
TRUE or FALSE? The antithetic random numbers TRUE
technique intentionally induces negative correlation
between two runs of the same system - this allows us to
better estimate the mean of the system.
TRUE or FALSE? The control variates technique provides TRUE
unbiased, low-variance estimates using a method
reminiscent of regression.
Statistical ranking and selection techniques have been All of the above.
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.
