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ISYE 6644 SIMULATION EXAM 2 STUDY GUIDE |
SPRING 2026 UPDATE | PRACTICE QUESTIONS
AND ANSWERS | EXAM REVIEW | 100%
CORRECT ANSWERS | VERIFIED SOLUTIONS
This practice examination is designed for students preparing for ISYE 6644
Simulation Exam 2 at Georgia Tech. It serves as a comprehensive study guide and
exam review, reflecting the latest update. The questions are crafted to mirror the
difficulty, quantitative rigor, and scope of the midterm examination, covering all
essential topics including random number generation, random variate generation,
input modeling, output analysis, variance reduction techniques, and simulation
optimization. By engaging with these practice questions and answers, students can
assess their readiness, identify knowledge gaps, and reinforce their understanding
of critical simulation concepts. The detailed rationales provide verified solutions,
ensuring a deep comprehension of the material and enhancing the effectiveness of
your preparation for this rigorous graduate-level examination.
Table of Contents
1. Random Number Generation
2. Random Variate Generation
3. Input Modeling and Goodness-of-Fit
4. Output Analysis for Terminating Simulations
5. Output Analysis for Steady-State Simulations
6. Variance Reduction Techniques
7. Simulation Optimization and Sensitivity Analysis
8. Special Topics in Simulation
, 2
Question 1: Which of the following is a common method for generating pseudo-
random numbers in simulation?
A) Inverse transform method
B) Linear congruential generator
C) Acceptance-rejection method
D) Box-Muller transformation
Correct Answer: B
The linear congruential generator (LCG) is a standard algorithm for generating
pseudo-random numbers. Option A is a method for generating random variates
from a distribution. Option C is a method for generating random variates. Option
D is a method for generating normal random variates.
Question 2: In an LCG defined by Xn+1=(aXn+c)mod mXn+1=(aXn+c)modm,
what condition is necessary to achieve a full period?
A) c=0c=0
B) a=1a=1
C) cc and mm are relatively prime
D) mm is prime
Correct Answer: C
For a full period (period = mm), the Hull-Dobell theorem requires that cc and mm
are relatively prime, a−1a−1 is divisible by all prime factors of mm, and if mm is
divisible by 4, a−1a−1 is divisible by 4. Option A gives a multiplicative LCG
which cannot achieve full period. Option B is not required. Option D is not
sufficient.
Question 3: What is the inverse transform method used for?
A) Generating random numbers uniformly
B) Generating random variates from a given distribution
C) Testing randomness of a sequence
D) Reducing variance in simulation
Correct Answer: B
The inverse transform method generates random variates from a distribution by
, 3
inverting its CDF. Option A is random number generation. Option C is statistical
testing. Option D is variance reduction.
Question 4: To generate an exponential random variable with rate λλ using inverse
transform, what is the correct formula given U∼Uniform(0,1)U∼Uniform(0,1)?
A) −ln(U)/λ−ln(U)/λ
B) −ln(1−U)/λ−ln(1−U)/λ
C) ln(U)/λln(U)/λ
D) U/λU/λ
Correct Answer: A
The inverse transform for exponential is X=−ln(U)/λX=−ln(U)/λ since
F(x)=1−e−λxF(x)=1−e−λx. Option B is also correct mathematically (since
1−U1−U is also uniform) but A is the standard form. Option C is negative. Option
D is incorrect.
Question 5: Which of the following is NOT a valid test for random number
generators?
A) Kolmogorov-Smirnov test
B) Chi-square test
C) Autocorrelation test
D) Acceptance-rejection test
Correct Answer: D
Acceptance-rejection is a method for generating random variates, not a test for
randomness. Options A, B, and C are all tests for randomness.
Question 6: The Box-Muller method is used to generate which type of random
variates?
A) Exponential
B) Normal
C) Poisson
D) Gamma
, 4
Correct Answer: B
The Box-Muller transformation generates standard normal random variates from
two independent uniform random variables. Options A, C, and D are generated by
other methods.
Question 7: In acceptance-rejection, what is the role of the majorizing function
g(x)g(x)?
A) It must be a probability density function
B) It must be greater than or equal to the target density f(x)f(x) for all xx
C) It must be easy to invert
D) It must be a normal distribution
Correct Answer: B
The majorizing function g(x)g(x) must satisfy f(x)≤c⋅g(x)f(x)≤c⋅g(x) for some
constant cc. It does not have to be a density (though often is), nor easy to invert,
nor normal.
Question 8: What is the composition method used for?
A) Generating random numbers
B) Generating random variates from a mixture distribution
C) Testing goodness-of-fit
D) Reducing variance
Correct Answer: B
Composition generates variates from a mixture by first selecting a component
distribution and then generating from it. Option A is random number generation.
Option C is input modeling. Option D is variance reduction.
Question 9: Which distribution is often used to model interarrival times in a
Poisson process?
A) Normal
B) Exponential
C) Uniform
D) Binomial
ISYE 6644 SIMULATION EXAM 2 STUDY GUIDE |
SPRING 2026 UPDATE | PRACTICE QUESTIONS
AND ANSWERS | EXAM REVIEW | 100%
CORRECT ANSWERS | VERIFIED SOLUTIONS
This practice examination is designed for students preparing for ISYE 6644
Simulation Exam 2 at Georgia Tech. It serves as a comprehensive study guide and
exam review, reflecting the latest update. The questions are crafted to mirror the
difficulty, quantitative rigor, and scope of the midterm examination, covering all
essential topics including random number generation, random variate generation,
input modeling, output analysis, variance reduction techniques, and simulation
optimization. By engaging with these practice questions and answers, students can
assess their readiness, identify knowledge gaps, and reinforce their understanding
of critical simulation concepts. The detailed rationales provide verified solutions,
ensuring a deep comprehension of the material and enhancing the effectiveness of
your preparation for this rigorous graduate-level examination.
Table of Contents
1. Random Number Generation
2. Random Variate Generation
3. Input Modeling and Goodness-of-Fit
4. Output Analysis for Terminating Simulations
5. Output Analysis for Steady-State Simulations
6. Variance Reduction Techniques
7. Simulation Optimization and Sensitivity Analysis
8. Special Topics in Simulation
, 2
Question 1: Which of the following is a common method for generating pseudo-
random numbers in simulation?
A) Inverse transform method
B) Linear congruential generator
C) Acceptance-rejection method
D) Box-Muller transformation
Correct Answer: B
The linear congruential generator (LCG) is a standard algorithm for generating
pseudo-random numbers. Option A is a method for generating random variates
from a distribution. Option C is a method for generating random variates. Option
D is a method for generating normal random variates.
Question 2: In an LCG defined by Xn+1=(aXn+c)mod mXn+1=(aXn+c)modm,
what condition is necessary to achieve a full period?
A) c=0c=0
B) a=1a=1
C) cc and mm are relatively prime
D) mm is prime
Correct Answer: C
For a full period (period = mm), the Hull-Dobell theorem requires that cc and mm
are relatively prime, a−1a−1 is divisible by all prime factors of mm, and if mm is
divisible by 4, a−1a−1 is divisible by 4. Option A gives a multiplicative LCG
which cannot achieve full period. Option B is not required. Option D is not
sufficient.
Question 3: What is the inverse transform method used for?
A) Generating random numbers uniformly
B) Generating random variates from a given distribution
C) Testing randomness of a sequence
D) Reducing variance in simulation
Correct Answer: B
The inverse transform method generates random variates from a distribution by
, 3
inverting its CDF. Option A is random number generation. Option C is statistical
testing. Option D is variance reduction.
Question 4: To generate an exponential random variable with rate λλ using inverse
transform, what is the correct formula given U∼Uniform(0,1)U∼Uniform(0,1)?
A) −ln(U)/λ−ln(U)/λ
B) −ln(1−U)/λ−ln(1−U)/λ
C) ln(U)/λln(U)/λ
D) U/λU/λ
Correct Answer: A
The inverse transform for exponential is X=−ln(U)/λX=−ln(U)/λ since
F(x)=1−e−λxF(x)=1−e−λx. Option B is also correct mathematically (since
1−U1−U is also uniform) but A is the standard form. Option C is negative. Option
D is incorrect.
Question 5: Which of the following is NOT a valid test for random number
generators?
A) Kolmogorov-Smirnov test
B) Chi-square test
C) Autocorrelation test
D) Acceptance-rejection test
Correct Answer: D
Acceptance-rejection is a method for generating random variates, not a test for
randomness. Options A, B, and C are all tests for randomness.
Question 6: The Box-Muller method is used to generate which type of random
variates?
A) Exponential
B) Normal
C) Poisson
D) Gamma
, 4
Correct Answer: B
The Box-Muller transformation generates standard normal random variates from
two independent uniform random variables. Options A, C, and D are generated by
other methods.
Question 7: In acceptance-rejection, what is the role of the majorizing function
g(x)g(x)?
A) It must be a probability density function
B) It must be greater than or equal to the target density f(x)f(x) for all xx
C) It must be easy to invert
D) It must be a normal distribution
Correct Answer: B
The majorizing function g(x)g(x) must satisfy f(x)≤c⋅g(x)f(x)≤c⋅g(x) for some
constant cc. It does not have to be a density (though often is), nor easy to invert,
nor normal.
Question 8: What is the composition method used for?
A) Generating random numbers
B) Generating random variates from a mixture distribution
C) Testing goodness-of-fit
D) Reducing variance
Correct Answer: B
Composition generates variates from a mixture by first selecting a component
distribution and then generating from it. Option A is random number generation.
Option C is input modeling. Option D is variance reduction.
Question 9: Which distribution is often used to model interarrival times in a
Poisson process?
A) Normal
B) Exponential
C) Uniform
D) Binomial
