ISYE 6644 LATEST 2026 QUESTIONS AND ANSWERS
SURE A+
✔✔Bernoulli probability selection problem - ✔✔Bunch of Bernoulli populations and find
the one with the best success probability
✔✔Multinomial cell selection problem - ✔✔
✔✔Normal means ranking and selection problem - ✔✔Bunch of normal distributions
and we want to find the one with the largest or smallest mean.
✔✔(10.2) "Assume unknown variance sigma^2". Probably will use t-distribution. -
✔✔True.
✔✔(10.2) If we have an i.i.d. normal sample of observations, X1,X2,...,Xn, what
probability distribution is most-commonly used to obtain confidence intervals for the
mean? - ✔✔t-distribution
✔✔(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. - ✔✔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.` -
✔✔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. - ✔✔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?? - ✔✔You do
✔✔Anithetic Random Numbers Method - ✔✔Used for negative correlation between
estimators. Opposite of CRN
✔✔CRN - ✔✔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. - ✔✔True
✔✔(10.8) TRUE or FALSE? The control variates technique provides unbiased, low-
variance estimates using a method reminiscent of regression. - ✔✔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. - ✔✔All of them
✔✔(10.10) What is a possible goal of an indifference-zone normal means selection
technique? - ✔✔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. - ✔✔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. - ✔✔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? - ✔✔From table, find P* = 0.9, Theta* = 1.4
and k = 3 competitors
SURE A+
✔✔Bernoulli probability selection problem - ✔✔Bunch of Bernoulli populations and find
the one with the best success probability
✔✔Multinomial cell selection problem - ✔✔
✔✔Normal means ranking and selection problem - ✔✔Bunch of normal distributions
and we want to find the one with the largest or smallest mean.
✔✔(10.2) "Assume unknown variance sigma^2". Probably will use t-distribution. -
✔✔True.
✔✔(10.2) If we have an i.i.d. normal sample of observations, X1,X2,...,Xn, what
probability distribution is most-commonly used to obtain confidence intervals for the
mean? - ✔✔t-distribution
✔✔(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. - ✔✔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.` -
✔✔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. - ✔✔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?? - ✔✔You do
✔✔Anithetic Random Numbers Method - ✔✔Used for negative correlation between
estimators. Opposite of CRN
✔✔CRN - ✔✔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. - ✔✔True
✔✔(10.8) TRUE or FALSE? The control variates technique provides unbiased, low-
variance estimates using a method reminiscent of regression. - ✔✔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. - ✔✔All of them
✔✔(10.10) What is a possible goal of an indifference-zone normal means selection
technique? - ✔✔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. - ✔✔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. - ✔✔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? - ✔✔From table, find P* = 0.9, Theta* = 1.4
and k = 3 competitors
