ISYE 6644 2 CERTIFICATION SCRIPT 2026
QUESTIONS WITH SOLUTIONS GRADED A+
◍ TRUE or FALSE? The times between Poisson( λ ) arrivals are i.i.d. Exp( λ
)..
Answer: TRUE. (... as long as ( λ ) doesn't change over time.)
◍ Suppose that U 1 , U 2 , ... , U 24 are i.i.d. PRNs. What is the approximate
distribution of X = 5 + 3 ∑ i = 1 24 U i?.
Answer: Nor(41,18)
◍ The runs "up and down" test is most often used to test for goodness-of-fit of
observations..
Answer: FALSE. It's a test for independence.
◍ 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..
Answer: 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? Sequential ranking-and-selection procedures are
designed to stop early if one alternative seems to be way out in front of the
others..
Answer: TRUE
◍ Suppose X is a discrete random variable that can take on four possible
values: −2, 1, 4, and 7. The associated probabilities are, respectively: 0.1,
0.3, 0.2, and 0.4. Find an expression in Arena to generate one observation
coming from this p.m.f..
Answer: DISC(−2, 0.1, 1, 0.4, 4, 0.6, 7, 1)
,◍ TRUE or FALSE? In Arena, it is only possible to use one resource at a time
in a PROCESS module..
Answer: FALSE
◍ TRUE or FALSE? Suppose that X 1 , X 2 , . . . , X n are consecutive waiting
times, and we define the sample mean X ¯ = ∑ i = 1 n X i / n. Then V a r ( X
¯ ) = V a r ( X i ) / n..
Answer: Very FALSE! (The issue is that correlation between the
observations messes up the variance of the sample mean. In fact, this is one
of the main reasons why output analysis is difficult!)
◍ What is the MSE of an estimator?.
Answer: ^2+
◍ TRUE or FALSE? In Arena, you can use the expression EXPO(3) to
generate exponential interarrival times having a mean of 3..
Answer: TRUE
◍ 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. If we use procedure M B E M, then the corresponding table in the
notes (with k = 3) tells us to take 126 samples (taste tests). Suppose we take
those samples sequentially and after 100 have been taken it turns out that 65
people prefer Coke, 25 love Pepsi, and 10 like Dr. Pepper. What to do?.
Answer: Stop the test now and declare with confidence of at least 90% that
Coke is the most-preferred.
◍ The multivariate normal distribution's covariance matrix ∑ can be
decomposed into the form ∑ = C C
T. What does the C informally stand for?.
Answer: Cholesky
◍ If is a Unif(0,1) random variable, what's the distribution of
−1/ (1− )?.
, Answer: Exp( )
◍ Suppose I use the method of overlapping batch means with sample size n =
10000 and batch size m = 500. Approximately how many degrees of
freedom will the resulting variance estimator have?.
Answer: Denote b = n/m = 20. You get approximately 3 2 (b − 1) = 28.5 d.f.
(Will also accept 3b/2 = 30 or anything reasonably close.)
◍ In Arena, you can use a single DECIDE module to route customers to that
one of four servers having the smallest queue..
Answer: TRUE
◍ Suppose that U and V are PRNs. Let X = U +
V. Simulate this 5000 times, and draw a histogram of the 5000 numbers.
What p.d.f. does the histogram look like?.
Answer: TriangularBy the lesson notes, we know that the 5000 Xi's are all
Triangular(0,1,2). Since we have a histogram of 5000 of these, it really
ought to look like a triangular p.d.f. Thus, the answer is (c).
◍ 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?.
Answer: 126Go to the table in the notes and pick off the entry for k=3,
P^ =0.90, and θ^ =1.4.
◍ TRUE or FALSE? In Arena, once an entity is defined, it is not possible to
change the priority in which it gets processed by a resource..
Answer: FALSE
◍ TRUE or FALSE? In Arena, it is not possible use a single DECIDE module
to randomly route customers to one of three or more destinations..
Answer: FALSE
◍ Suppose A and B are two identically distributed, unbiased, antithetic
QUESTIONS WITH SOLUTIONS GRADED A+
◍ TRUE or FALSE? The times between Poisson( λ ) arrivals are i.i.d. Exp( λ
)..
Answer: TRUE. (... as long as ( λ ) doesn't change over time.)
◍ Suppose that U 1 , U 2 , ... , U 24 are i.i.d. PRNs. What is the approximate
distribution of X = 5 + 3 ∑ i = 1 24 U i?.
Answer: Nor(41,18)
◍ The runs "up and down" test is most often used to test for goodness-of-fit of
observations..
Answer: FALSE. It's a test for independence.
◍ 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..
Answer: 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? Sequential ranking-and-selection procedures are
designed to stop early if one alternative seems to be way out in front of the
others..
Answer: TRUE
◍ Suppose X is a discrete random variable that can take on four possible
values: −2, 1, 4, and 7. The associated probabilities are, respectively: 0.1,
0.3, 0.2, and 0.4. Find an expression in Arena to generate one observation
coming from this p.m.f..
Answer: DISC(−2, 0.1, 1, 0.4, 4, 0.6, 7, 1)
,◍ TRUE or FALSE? In Arena, it is only possible to use one resource at a time
in a PROCESS module..
Answer: FALSE
◍ TRUE or FALSE? Suppose that X 1 , X 2 , . . . , X n are consecutive waiting
times, and we define the sample mean X ¯ = ∑ i = 1 n X i / n. Then V a r ( X
¯ ) = V a r ( X i ) / n..
Answer: Very FALSE! (The issue is that correlation between the
observations messes up the variance of the sample mean. In fact, this is one
of the main reasons why output analysis is difficult!)
◍ What is the MSE of an estimator?.
Answer: ^2+
◍ TRUE or FALSE? In Arena, you can use the expression EXPO(3) to
generate exponential interarrival times having a mean of 3..
Answer: TRUE
◍ 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. If we use procedure M B E M, then the corresponding table in the
notes (with k = 3) tells us to take 126 samples (taste tests). Suppose we take
those samples sequentially and after 100 have been taken it turns out that 65
people prefer Coke, 25 love Pepsi, and 10 like Dr. Pepper. What to do?.
Answer: Stop the test now and declare with confidence of at least 90% that
Coke is the most-preferred.
◍ The multivariate normal distribution's covariance matrix ∑ can be
decomposed into the form ∑ = C C
T. What does the C informally stand for?.
Answer: Cholesky
◍ If is a Unif(0,1) random variable, what's the distribution of
−1/ (1− )?.
, Answer: Exp( )
◍ Suppose I use the method of overlapping batch means with sample size n =
10000 and batch size m = 500. Approximately how many degrees of
freedom will the resulting variance estimator have?.
Answer: Denote b = n/m = 20. You get approximately 3 2 (b − 1) = 28.5 d.f.
(Will also accept 3b/2 = 30 or anything reasonably close.)
◍ In Arena, you can use a single DECIDE module to route customers to that
one of four servers having the smallest queue..
Answer: TRUE
◍ Suppose that U and V are PRNs. Let X = U +
V. Simulate this 5000 times, and draw a histogram of the 5000 numbers.
What p.d.f. does the histogram look like?.
Answer: TriangularBy the lesson notes, we know that the 5000 Xi's are all
Triangular(0,1,2). Since we have a histogram of 5000 of these, it really
ought to look like a triangular p.d.f. Thus, the answer is (c).
◍ 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?.
Answer: 126Go to the table in the notes and pick off the entry for k=3,
P^ =0.90, and θ^ =1.4.
◍ TRUE or FALSE? In Arena, once an entity is defined, it is not possible to
change the priority in which it gets processed by a resource..
Answer: FALSE
◍ TRUE or FALSE? In Arena, it is not possible use a single DECIDE module
to randomly route customers to one of three or more destinations..
Answer: FALSE
◍ Suppose A and B are two identically distributed, unbiased, antithetic
