ISYE 6644 Summer 2025-2026 Final Exam
Graded A
What is a possible goal of an indifference-zone normal means selection
technique? - answer-Find 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. - answer-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. - answer-True
Which of the following problems might best be characterized by a finite-
horizon simulation? - answer-Simulating the operations of a bank from 9:00
a.m. until 5:00 p.m.
,Let's run a simulation whose output is a sequence of daily inventory levels for a
particular product. Which of the following statements is true? - answer-The
consecutive daily inventory levels may not be identically distributed.
Suppose that X 1 , X 2 , ... is a stationary (steady-state) stochastic process with
covariance function R k ≡ C o v ( X 1 , X 1 + k ), for k = 0 , 1 , .... We know from
class that the variance of the sample mean can be represented asV a r ( X ¯ n )
= 1 n * R 0 + 2 ∑ k = 1 n − 1 ( 1 − k n ) R k + .We also know from class that for a
simple AR(1) process, we have R k = ϕ k, k = 0 , 1 , 2 , ... Compute V a r ( X ¯ n )
for an AR(1) process with n = 3 and ϕ = 0.8. - answer-0.831
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? - answer-50
batches of 2000 observations
because the method of batch means requires a very large batch size
Consider the output analysis method of non overlapping batch means.
Assuming that you have a sufficiently large batch size, it can be shown that
when the number of batches b is even, the expected width of the 90% two-
sided confidence interval for μ is proportional tot 0.05 , b − 1 b − 1 ( b − 1 2 ) ( b
, − 3 2 ) ⋯ 1 2 ( b − 2 2 ) ! .Using the above equation, determine which of the
following values of b gives the smallest expected width. - answer-b=6
Let h ( b ) denote the value of the above expression as a function of b. Then
easy calculations reveal that h ( b ) = 3.157, h ( 4 ) = 1.019, and h ( 6 ) = 0.845.
So the answer is b = 6
Consider the following observations:
54 70 75 62
If we choose a batch size of 3, calculate all of the overlapping batch means for
me. - answer-66.3, 69.0
X1,3 = 1/3 ΣXi = 66.3 and
X2,3 = 1/3 ΣXi = 69.
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. - answer-All three of (b), (c), and (d).
Graded A
What is a possible goal of an indifference-zone normal means selection
technique? - answer-Find 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. - answer-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. - answer-True
Which of the following problems might best be characterized by a finite-
horizon simulation? - answer-Simulating the operations of a bank from 9:00
a.m. until 5:00 p.m.
,Let's run a simulation whose output is a sequence of daily inventory levels for a
particular product. Which of the following statements is true? - answer-The
consecutive daily inventory levels may not be identically distributed.
Suppose that X 1 , X 2 , ... is a stationary (steady-state) stochastic process with
covariance function R k ≡ C o v ( X 1 , X 1 + k ), for k = 0 , 1 , .... We know from
class that the variance of the sample mean can be represented asV a r ( X ¯ n )
= 1 n * R 0 + 2 ∑ k = 1 n − 1 ( 1 − k n ) R k + .We also know from class that for a
simple AR(1) process, we have R k = ϕ k, k = 0 , 1 , 2 , ... Compute V a r ( X ¯ n )
for an AR(1) process with n = 3 and ϕ = 0.8. - answer-0.831
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? - answer-50
batches of 2000 observations
because the method of batch means requires a very large batch size
Consider the output analysis method of non overlapping batch means.
Assuming that you have a sufficiently large batch size, it can be shown that
when the number of batches b is even, the expected width of the 90% two-
sided confidence interval for μ is proportional tot 0.05 , b − 1 b − 1 ( b − 1 2 ) ( b
, − 3 2 ) ⋯ 1 2 ( b − 2 2 ) ! .Using the above equation, determine which of the
following values of b gives the smallest expected width. - answer-b=6
Let h ( b ) denote the value of the above expression as a function of b. Then
easy calculations reveal that h ( b ) = 3.157, h ( 4 ) = 1.019, and h ( 6 ) = 0.845.
So the answer is b = 6
Consider the following observations:
54 70 75 62
If we choose a batch size of 3, calculate all of the overlapping batch means for
me. - answer-66.3, 69.0
X1,3 = 1/3 ΣXi = 66.3 and
X2,3 = 1/3 ΣXi = 69.
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. - answer-All three of (b), (c), and (d).
