ISYE 6644 OAN 1 SIMULATION FINAL TEST
2026 QUESTIONS WITH CORRECT
ANSWERS GRADED A+
◍ Terminating Simulation.
Answer: A simulation where the system's behavior is of interest only for a
finite duration or until a specific event occurs.
◍ Suppose that you want to pick that one of three normal populations having
the largest mean. We'll assume that the variances of the three competitors
are all known to be equal to σ 2 = 4. (Ya, I know that this is a crazy,
unrealistic assumption, but let's go with it anyway, okey dokey?) I want to
choose the best of the three populations with probability of correct selection
of 95% whenever the best population's mean happens to be at least δ = 1
larger than the second-best population's. How many observations from each
population does Bechhofer's procedure N B tell me to take before I can
make such a conclusion?.
Answer: Using the notation of the notes, we want to make sure to get the
right answer with probability of P = 0.95 whenever μ [ k ] − μ [ k − 1 ] ≥
δ = 1. We simply go to NB's table with k = 3 and δ / σ = to obtain
a sample size of n = 30 from each population.
◍ Find the sample variance of -3, -2, -1, 0,1,2,3.
Answer: 14/3S^2 formula
◍ Consider the time series Y i = ϕ Y i − 1 + ϵ i , i = 1 , 2 , ..., where the ϵ i's
are i.i.d. normal. What is this time series called? (Give the best answer.).
Answer: first-order autoregressive process
◍ Let's play Name That Distribution!The number of times a "3" comes up in
10 dice tosses..
, Answer: Binomial
◍ Output Analysis.
Answer: The process of analyzing the data generated by a simulation to
draw statistically valid conclusions about the system being modeled.
◍ Simulation Methods.
Answer: Techniques that involve imitating the operation of a system over
time to study its behavior and draw inferences.
◍ Inverse Transform Method.
Answer: A technique for generating random variates from a specific
distribution by using the inverse of its cumulative distribution function
applied to a Unif(0,1) random number.
◍ Dynamic Model.
Answer: A model that evolves or changes over time.
◍ Consider the PRN's U 1 = 0.1 , U 2 = 0.9 , and U 3 = 0.2. Use
Kolmogorov-Smirnov with α = 0.05 to test to see if these numbers are
indeed uniform. Do we ACCEPT or REJECT uniformity?.
Answer: AcceptSince D < D α , n, we ACCEPT uniformity (though it's kind
of a joke since it's only based on 3 observations)
◍ True or False? The A-R algorithm for X~Pois(λ) tells us to generate PRNs
until e^-λ .... Ui for the first time, and then set X=n..
Answer: TRUE. Yup - that's how you do it (though sometimes it's a bit
tedious if λ is large).
◍ Simulation Model.
Answer: A high-level representation used to imitate the operation of a
real-world process or system over time.
◍ If is Unif(0,1), what is 6 ? (Note that . is the round-up function.).
Answer: A 6-side die toss
◍ Independent Replications.
Answer: A method for analyzing terminating simulations by running the
, simulation multiple times with different random number streams to obtain
independent observations of system performance.
◍ Simulation Languages.
Answer: Specialized software packages designed to facilitate the building
and running of simulation models (e.g., Arena).
◍ Suppose that U 1 , U 2 , ... , U 5000 are i.i.d. Unif(0,1) random variables.
Using Excel (or your favorite programming language), simulate X i = − ln
( U i ) for i = 1 , 2 , ... , 5000. Draw a histogram of the 5000 numbers.
What p.d.f. does the histogram look like?.
Answer: Exponential
◍ 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).
◍ 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.
◍ Validation.
Answer: The process of determining whether the simulation model is an
accurate representation of the real-world system being studied.
◍ Stochastic Model.
Answer: A model that incorporates randomness or probability into its
operation.
2026 QUESTIONS WITH CORRECT
ANSWERS GRADED A+
◍ Terminating Simulation.
Answer: A simulation where the system's behavior is of interest only for a
finite duration or until a specific event occurs.
◍ Suppose that you want to pick that one of three normal populations having
the largest mean. We'll assume that the variances of the three competitors
are all known to be equal to σ 2 = 4. (Ya, I know that this is a crazy,
unrealistic assumption, but let's go with it anyway, okey dokey?) I want to
choose the best of the three populations with probability of correct selection
of 95% whenever the best population's mean happens to be at least δ = 1
larger than the second-best population's. How many observations from each
population does Bechhofer's procedure N B tell me to take before I can
make such a conclusion?.
Answer: Using the notation of the notes, we want to make sure to get the
right answer with probability of P = 0.95 whenever μ [ k ] − μ [ k − 1 ] ≥
δ = 1. We simply go to NB's table with k = 3 and δ / σ = to obtain
a sample size of n = 30 from each population.
◍ Find the sample variance of -3, -2, -1, 0,1,2,3.
Answer: 14/3S^2 formula
◍ Consider the time series Y i = ϕ Y i − 1 + ϵ i , i = 1 , 2 , ..., where the ϵ i's
are i.i.d. normal. What is this time series called? (Give the best answer.).
Answer: first-order autoregressive process
◍ Let's play Name That Distribution!The number of times a "3" comes up in
10 dice tosses..
, Answer: Binomial
◍ Output Analysis.
Answer: The process of analyzing the data generated by a simulation to
draw statistically valid conclusions about the system being modeled.
◍ Simulation Methods.
Answer: Techniques that involve imitating the operation of a system over
time to study its behavior and draw inferences.
◍ Inverse Transform Method.
Answer: A technique for generating random variates from a specific
distribution by using the inverse of its cumulative distribution function
applied to a Unif(0,1) random number.
◍ Dynamic Model.
Answer: A model that evolves or changes over time.
◍ Consider the PRN's U 1 = 0.1 , U 2 = 0.9 , and U 3 = 0.2. Use
Kolmogorov-Smirnov with α = 0.05 to test to see if these numbers are
indeed uniform. Do we ACCEPT or REJECT uniformity?.
Answer: AcceptSince D < D α , n, we ACCEPT uniformity (though it's kind
of a joke since it's only based on 3 observations)
◍ True or False? The A-R algorithm for X~Pois(λ) tells us to generate PRNs
until e^-λ .... Ui for the first time, and then set X=n..
Answer: TRUE. Yup - that's how you do it (though sometimes it's a bit
tedious if λ is large).
◍ Simulation Model.
Answer: A high-level representation used to imitate the operation of a
real-world process or system over time.
◍ If is Unif(0,1), what is 6 ? (Note that . is the round-up function.).
Answer: A 6-side die toss
◍ Independent Replications.
Answer: A method for analyzing terminating simulations by running the
, simulation multiple times with different random number streams to obtain
independent observations of system performance.
◍ Simulation Languages.
Answer: Specialized software packages designed to facilitate the building
and running of simulation models (e.g., Arena).
◍ Suppose that U 1 , U 2 , ... , U 5000 are i.i.d. Unif(0,1) random variables.
Using Excel (or your favorite programming language), simulate X i = − ln
( U i ) for i = 1 , 2 , ... , 5000. Draw a histogram of the 5000 numbers.
What p.d.f. does the histogram look like?.
Answer: Exponential
◍ 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).
◍ 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.
◍ Validation.
Answer: The process of determining whether the simulation model is an
accurate representation of the real-world system being studied.
◍ Stochastic Model.
Answer: A model that incorporates randomness or probability into its
operation.
