ISYE 6644 - FINAL PREP QUESTIONS
& ANSWERS(RATED A+)
What is a possible goal of an indifference-zone normal means selection technique?
- ANSWERFind the normal population having the largest mean, especially if the
largest mean is ≫ the second-largest.
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. - ANSWERTrue
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. - ANSWERTrue
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. - ANSWERAll 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? - ANSWER1) 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? - ANSWERFind 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? - ANSWER126
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 - ANSWERAll 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? -
ANSWERt
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. -
ANSWERFALSE. {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. -
ANSWERTRUE
TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-𝑡confidence interval. -
ANSWERTRUE
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?? - ANSWERYou 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. - ANSWERTRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression. - ANSWERTRUE
Suppose we want to estimate the expected average waiting time for the first m = 100
customers at a bank. We make r = 4 independent replications of the system, each
initialized empty and idle and consisting of 100 waiting times. The resulting replicate
means are:
i 1 2 3 4 Z i 5.2 4.3 3.1 4.2
Find a 90% confidence interval for the mean average waiting time for the first 100
customers. - ANSWER[3.188,5.212]
Consider a particular data set of 100,000 stationary waiting times obtained from a
large queueing system. Suppose your goal is to get a confidence interval for the
unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b)
10000 batches of 10 observations each? - ANSWER50 batches of 2000
observations
because the method of batch means requires a very large batch size
& ANSWERS(RATED A+)
What is a possible goal of an indifference-zone normal means selection technique?
- ANSWERFind the normal population having the largest mean, especially if the
largest mean is ≫ the second-largest.
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. - ANSWERTrue
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. - ANSWERTrue
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. - ANSWERAll 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? - ANSWER1) 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? - ANSWERFind 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? - ANSWER126
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 - ANSWERAll 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? -
ANSWERt
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. -
ANSWERFALSE. {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. -
ANSWERTRUE
TRUE or FALSE? The common random numbers technique intentionally induces
positive correlation between two systems - much like a paired-𝑡confidence interval. -
ANSWERTRUE
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?? - ANSWERYou 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. - ANSWERTRUE
TRUE or FALSE? The control variates technique provides unbiased, low-variance
estimates using a method reminiscent of regression. - ANSWERTRUE
Suppose we want to estimate the expected average waiting time for the first m = 100
customers at a bank. We make r = 4 independent replications of the system, each
initialized empty and idle and consisting of 100 waiting times. The resulting replicate
means are:
i 1 2 3 4 Z i 5.2 4.3 3.1 4.2
Find a 90% confidence interval for the mean average waiting time for the first 100
customers. - ANSWER[3.188,5.212]
Consider a particular data set of 100,000 stationary waiting times obtained from a
large queueing system. Suppose your goal is to get a confidence interval for the
unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b)
10000 batches of 10 observations each? - ANSWER50 batches of 2000
observations
because the method of batch means requires a very large batch size
