COMS 5583 EXAM PREPARATION TEST BANK WITH
CORRECT ANSWERS
SECTION I: SIMULATION FUNDAMENTALS & APPLICATIONS
1. Simulation can be used to analyze supply-chain models too complicated to
solve analytically.
A) True
B) False
Correct Answer: A
Rationale: Simulation is particularly valuable when analytical solutions are
intractable. Supply-chain models with stochastic demand, multiple stages, and
complex routing policies often defy closed-form analysis. Discrete-event
simulation allows analysts to model these systems directly and estimate
performance measures through repeated sampling.
2. Which of the following is NOT a primary advantage of using simulation over
analytical modeling?
A) Ability to model complex, nonlinear relationships
B) Provides exact closed-form solutions
C) Allows experimentation without disrupting the real system
D) Can incorporate stochastic variability
Correct Answer: B
Rationale: Simulation does not provide exact closed-form solutions; it
provides numerical estimates subject to sampling error. Analytical models yield
exact solutions. Simulation's advantages include handling complexity,
experimentation safety, and stochastic modeling.
3. (SATA) Which of the following scenarios are appropriate applications of
simulation? Select all that apply.
,A) Evaluating a new hospital emergency department layout before construction
B) Computing the exact derivative of a polynomial
C) Estimating the probability of bankruptcy for a startup under uncertain revenue
D) Solving a system of linear equations with a unique solution
Correct Answers: A, C
Rationale: Simulation excels when the system is stochastic or complex.
Hospital layout evaluation and startup bankruptcy probability both involve
uncertainty and complexity. Computing exact derivatives and solving well-posed
linear systems are deterministic mathematical operations better handled
analytically.
4. In a discrete-event simulation, the simulation clock advances:
A) By fixed time increments regardless of events
B) From one event time to the next event time
C) Continuously in real time
D) Only when the user presses "step"
Correct Answer: B
Rationale: Discrete-event simulation uses next-event time advance,
where the clock jumps to the time of the next scheduled event. This is more
efficient than fixed-increment time advance because no time is wasted examining
periods with no state changes.
5. A simulation study produces a 95% confidence interval for mean waiting time
of [12.3, 18.7] minutes. Which interpretation is correct?
A) 95% of customers wait between 12.3 and 18.7 minutes
B) The true mean waiting time is definitely in this interval
C) If we repeated the simulation many times, 95% of such intervals would contain
the true mean
D) The sample mean is 95% likely to be 15.5
, Correct Answer: C
Rationale: A confidence interval is a statement about the procedure, not
about a single interval. The correct frequentist interpretation is that 95% of
intervals constructed this way would contain the true parameter. The interval
either does or does not contain the true mean—we cannot assign a probability to
that for a realized interval.
6. (SATA) Which of the following are legitimate uses of common random numbers
(CRN) in simulation? Select all that apply.
A) Comparing two system designs under identical random conditions
B) Reducing variance when estimating the difference between two system means
C) Eliminating all randomness from the simulation
D) Inducing positive correlation between paired outputs
Correct Answers: A, B, D
Rationale: Common random numbers are used to compare systems under
identical stochastic conditions, reduce variance of difference estimators by
inducing positive correlation, and improve precision. CRN does not eliminate
randomness; it synchronizes it.
7. If two systems are simulated independently, the variance of the difference in
sample means is:
A) Var(X̄₁) − Var(X̄₂)
B) Var(X̄₁) + Var(X̄₂)
C) Var(X̄₁) + Var(X̄₂) − 2Cov(X̄₁, X̄₂)
D) √(Var(X̄₁) + Var(X̄₂))
Correct Answer: C
Rationale: The general formula for the variance of a difference is Var(A −
B) = Var(A) + Var(B) − 2Cov(A, B). When independent, Cov = 0 and this reduces to
, Var(A) + Var(B). With CRN, the positive covariance reduces the variance of the
difference.
8. Using common random numbers to compare two systems typically produces a
covariance that is:
A) Negative
B) Zero
C) Positive
D) Undefined
Correct Answer: C
Rationale: CRN induces positive correlation between the outputs of the
two systems because they experience the same random inputs. This positive
covariance reduces Var(X̄₁ − X̄₂), making the comparison more precise.
9. Suppose A and B are identically distributed, unbiased, antithetic estimators for
μ, and C = (A + B)/2. Which is true?
A) E[C] = μ and Var(C) = Var(A)/2
B) E[C] = μ and Var(C) < Var(A)/2
C) E[C] = μ/2 and Var(C) = Var(A)
D) E[C] ≠ μ
Correct Answer: B
Rationale: Antithetic variates induce negative correlation between A and
B. Since E[A] = E[B] = μ, E[C] = μ. Var(C) = [Var(A) + Var(B) + 2Cov(A,B)]/4. With
negative covariance, Var(C) < Var(A)/2.
10. A paired-t confidence interval is appropriate when:
A) Samples from two populations are independent
B) Samples are naturally paired and differences are approximately normal
CORRECT ANSWERS
SECTION I: SIMULATION FUNDAMENTALS & APPLICATIONS
1. Simulation can be used to analyze supply-chain models too complicated to
solve analytically.
A) True
B) False
Correct Answer: A
Rationale: Simulation is particularly valuable when analytical solutions are
intractable. Supply-chain models with stochastic demand, multiple stages, and
complex routing policies often defy closed-form analysis. Discrete-event
simulation allows analysts to model these systems directly and estimate
performance measures through repeated sampling.
2. Which of the following is NOT a primary advantage of using simulation over
analytical modeling?
A) Ability to model complex, nonlinear relationships
B) Provides exact closed-form solutions
C) Allows experimentation without disrupting the real system
D) Can incorporate stochastic variability
Correct Answer: B
Rationale: Simulation does not provide exact closed-form solutions; it
provides numerical estimates subject to sampling error. Analytical models yield
exact solutions. Simulation's advantages include handling complexity,
experimentation safety, and stochastic modeling.
3. (SATA) Which of the following scenarios are appropriate applications of
simulation? Select all that apply.
,A) Evaluating a new hospital emergency department layout before construction
B) Computing the exact derivative of a polynomial
C) Estimating the probability of bankruptcy for a startup under uncertain revenue
D) Solving a system of linear equations with a unique solution
Correct Answers: A, C
Rationale: Simulation excels when the system is stochastic or complex.
Hospital layout evaluation and startup bankruptcy probability both involve
uncertainty and complexity. Computing exact derivatives and solving well-posed
linear systems are deterministic mathematical operations better handled
analytically.
4. In a discrete-event simulation, the simulation clock advances:
A) By fixed time increments regardless of events
B) From one event time to the next event time
C) Continuously in real time
D) Only when the user presses "step"
Correct Answer: B
Rationale: Discrete-event simulation uses next-event time advance,
where the clock jumps to the time of the next scheduled event. This is more
efficient than fixed-increment time advance because no time is wasted examining
periods with no state changes.
5. A simulation study produces a 95% confidence interval for mean waiting time
of [12.3, 18.7] minutes. Which interpretation is correct?
A) 95% of customers wait between 12.3 and 18.7 minutes
B) The true mean waiting time is definitely in this interval
C) If we repeated the simulation many times, 95% of such intervals would contain
the true mean
D) The sample mean is 95% likely to be 15.5
, Correct Answer: C
Rationale: A confidence interval is a statement about the procedure, not
about a single interval. The correct frequentist interpretation is that 95% of
intervals constructed this way would contain the true parameter. The interval
either does or does not contain the true mean—we cannot assign a probability to
that for a realized interval.
6. (SATA) Which of the following are legitimate uses of common random numbers
(CRN) in simulation? Select all that apply.
A) Comparing two system designs under identical random conditions
B) Reducing variance when estimating the difference between two system means
C) Eliminating all randomness from the simulation
D) Inducing positive correlation between paired outputs
Correct Answers: A, B, D
Rationale: Common random numbers are used to compare systems under
identical stochastic conditions, reduce variance of difference estimators by
inducing positive correlation, and improve precision. CRN does not eliminate
randomness; it synchronizes it.
7. If two systems are simulated independently, the variance of the difference in
sample means is:
A) Var(X̄₁) − Var(X̄₂)
B) Var(X̄₁) + Var(X̄₂)
C) Var(X̄₁) + Var(X̄₂) − 2Cov(X̄₁, X̄₂)
D) √(Var(X̄₁) + Var(X̄₂))
Correct Answer: C
Rationale: The general formula for the variance of a difference is Var(A −
B) = Var(A) + Var(B) − 2Cov(A, B). When independent, Cov = 0 and this reduces to
, Var(A) + Var(B). With CRN, the positive covariance reduces the variance of the
difference.
8. Using common random numbers to compare two systems typically produces a
covariance that is:
A) Negative
B) Zero
C) Positive
D) Undefined
Correct Answer: C
Rationale: CRN induces positive correlation between the outputs of the
two systems because they experience the same random inputs. This positive
covariance reduces Var(X̄₁ − X̄₂), making the comparison more precise.
9. Suppose A and B are identically distributed, unbiased, antithetic estimators for
μ, and C = (A + B)/2. Which is true?
A) E[C] = μ and Var(C) = Var(A)/2
B) E[C] = μ and Var(C) < Var(A)/2
C) E[C] = μ/2 and Var(C) = Var(A)
D) E[C] ≠ μ
Correct Answer: B
Rationale: Antithetic variates induce negative correlation between A and
B. Since E[A] = E[B] = μ, E[C] = μ. Var(C) = [Var(A) + Var(B) + 2Cov(A,B)]/4. With
negative covariance, Var(C) < Var(A)/2.
10. A paired-t confidence interval is appropriate when:
A) Samples from two populations are independent
B) Samples are naturally paired and differences are approximately normal
