1
ISYE 6644 Final Exam – Simulation and Modeling for
Engineering and Science Questions 1–220 | Advanced / Hard |
Graduate-Level Engineering Students
1 Which of the following best characterizes a discrete-event dynamic system?
A. The state variables change continuously over time according to differential equations.
B. The state variables change only at discrete points in time when events occur.
C. The system evolves in discrete time steps regardless of event occurrences.
D. The system is deterministic and does not involve any randomness.
Correct Answer: B
Explanation: Discrete-event dynamic systems are characterized by state changes that occur only
at discrete points in time, triggered by specific events. Option A describes continuous systems, C
describes time-stepped simulation, and D incorrectly suggests determinism.
2 In the context of simulation, which of the following is NOT a valid reason for using simulation
over analytical methods?
,2
A. The system is too complex to be modeled analytically.
B. Simulation allows for "what-if" analysis under various scenarios.
C. Simulation always provides exact optimal solutions.
D. Analytical solutions may not exist for stochastic systems.
Correct Answer: C
Explanation: Simulation does not guarantee optimal solutions; it provides estimates of system
performance. Options A, B, and D are all valid motivations for using simulation. Analytical
methods, when available, typically yield exact solutions, but many complex stochastic systems
lack closed-form analytical solutions.
3 Let X be a continuous random variable with probability density function f(x) = 2x for 0 < x < 1,
and 0 otherwise. What is the expected value E[X]?
A. 1/3
B. 1/2
C. 2/3
D. 3/4
,3
Correct Answer: C
Explanation: E[X] = ∫₀¹ x · 2x dx = ∫₀¹ 2x² dx = 2/3. Option A (1/3) would be the result if the
density were f(x) = 2(1-x). Option B (1/2) is the mean of Uniform(0,1). Option D (3/4) is incorrect.
4 Which of the following statements about the exponential distribution is FALSE?
A. It has the memoryless property.
B. Its mean equals its standard deviation.
C. It is a common choice for modeling inter-arrival times in queueing systems.
D. Its coefficient of variation is always greater than 1.
Correct Answer: D
Explanation: For an exponential distribution with rate λ, the mean is 1/λ and the standard
deviation is 1/λ, so the coefficient of variation (CV) is 1, not greater than 1. Options A, B, and C
are all true statements about the exponential distribution.
5 A linear congruential generator (LCG) is defined by Xᵢ = (aXᵢ₋₁ + c) mod m. Which condition is
necessary for the generator to achieve full period?
, 4
A. c = 0
B. m is prime
C. gcd(c, m) = 1
D. a ≡ 1 mod 4
Correct Answer: C
Explanation: For full period in an LCG, the Hull-Dobell theorem requires: (1) gcd(c, m) = 1, (2) a ≡
1 mod p for every prime p dividing m, and (3) a ≡ 1 mod 4 if 4 divides m. Option C is one of these
necessary conditions. Option A would make it a multiplicative generator (not full period
generally). Option B is not required, and D is only one part of the condition.
6 In the inverse transform method for generating random variates from a continuous
distribution with CDF F, which of the following is the correct procedure?
A. Generate U ~ Uniform(0,1) and set X = F(U)
B. Generate U ~ Uniform(0,1) and set X = F⁻¹(U)
C. Generate U ~ Uniform(0,1) and set X = 1 - F(U)
D. Generate X directly from the PDF without using uniform random numbers
ISYE 6644 Final Exam – Simulation and Modeling for
Engineering and Science Questions 1–220 | Advanced / Hard |
Graduate-Level Engineering Students
1 Which of the following best characterizes a discrete-event dynamic system?
A. The state variables change continuously over time according to differential equations.
B. The state variables change only at discrete points in time when events occur.
C. The system evolves in discrete time steps regardless of event occurrences.
D. The system is deterministic and does not involve any randomness.
Correct Answer: B
Explanation: Discrete-event dynamic systems are characterized by state changes that occur only
at discrete points in time, triggered by specific events. Option A describes continuous systems, C
describes time-stepped simulation, and D incorrectly suggests determinism.
2 In the context of simulation, which of the following is NOT a valid reason for using simulation
over analytical methods?
,2
A. The system is too complex to be modeled analytically.
B. Simulation allows for "what-if" analysis under various scenarios.
C. Simulation always provides exact optimal solutions.
D. Analytical solutions may not exist for stochastic systems.
Correct Answer: C
Explanation: Simulation does not guarantee optimal solutions; it provides estimates of system
performance. Options A, B, and D are all valid motivations for using simulation. Analytical
methods, when available, typically yield exact solutions, but many complex stochastic systems
lack closed-form analytical solutions.
3 Let X be a continuous random variable with probability density function f(x) = 2x for 0 < x < 1,
and 0 otherwise. What is the expected value E[X]?
A. 1/3
B. 1/2
C. 2/3
D. 3/4
,3
Correct Answer: C
Explanation: E[X] = ∫₀¹ x · 2x dx = ∫₀¹ 2x² dx = 2/3. Option A (1/3) would be the result if the
density were f(x) = 2(1-x). Option B (1/2) is the mean of Uniform(0,1). Option D (3/4) is incorrect.
4 Which of the following statements about the exponential distribution is FALSE?
A. It has the memoryless property.
B. Its mean equals its standard deviation.
C. It is a common choice for modeling inter-arrival times in queueing systems.
D. Its coefficient of variation is always greater than 1.
Correct Answer: D
Explanation: For an exponential distribution with rate λ, the mean is 1/λ and the standard
deviation is 1/λ, so the coefficient of variation (CV) is 1, not greater than 1. Options A, B, and C
are all true statements about the exponential distribution.
5 A linear congruential generator (LCG) is defined by Xᵢ = (aXᵢ₋₁ + c) mod m. Which condition is
necessary for the generator to achieve full period?
, 4
A. c = 0
B. m is prime
C. gcd(c, m) = 1
D. a ≡ 1 mod 4
Correct Answer: C
Explanation: For full period in an LCG, the Hull-Dobell theorem requires: (1) gcd(c, m) = 1, (2) a ≡
1 mod p for every prime p dividing m, and (3) a ≡ 1 mod 4 if 4 divides m. Option C is one of these
necessary conditions. Option A would make it a multiplicative generator (not full period
generally). Option B is not required, and D is only one part of the condition.
6 In the inverse transform method for generating random variates from a continuous
distribution with CDF F, which of the following is the correct procedure?
A. Generate U ~ Uniform(0,1) and set X = F(U)
B. Generate U ~ Uniform(0,1) and set X = F⁻¹(U)
C. Generate U ~ Uniform(0,1) and set X = 1 - F(U)
D. Generate X directly from the PDF without using uniform random numbers
