ISYE 6644 OH Exam 2 Practice Questions – Spring 2025 Complete Study Guide with Verified Questions, Answers & Rationales. Georgia Institute Of Technology.

ISYE 6644 OH Exam 2 Practice Questions –
Spring 2025 Complete Study Guide with
Verified Questions, Answers & Rationales.
Georgia Institute Of Technology.




Section 1: Output Analysis and Statistical Estimation
Question 1
We often distinguish between two general types of simulations with regard to output
analysis. What are they called?

 A. Discrete and continuous
 B. Deterministic and stochastic
 C. Finite-horizon and steady-state
 D. Terminating and non-terminating

Correct Answer: C
Explanation: Finite-horizon (terminating) simulations have a natural stopping time (e.g.,
8:00 a.m. to 5:00 p.m.), while steady-state (non-terminating) simulations run indefinitely
to analyze long-run behavior .

Question 2
Which scenario is best suited for a finite-horizon analysis?

 A. Simulate an assembly line working 24/7
 B. Simulate bank operations from 8:00 a.m. to 5:00 p.m.
 C. Simulate a manufacturing plant with continuous production
 D. Simulate a call center that never closes

Correct Answer: B
Explanation: Bank operations from opening to closing have a natural termination time,
making it a finite-horizon simulation .

, Question 3
Which scenario is best suited for a steady-state analysis?

 A. Simulate an assembly line working 24/7
 B. Simulate a bank from 9:00 a.m. to 5:00 p.m.
 C. Simulate a one-day sale event
 D. Simulate a single customer visit

Correct Answer: A
Explanation: An assembly line running continuously (24/7) is analyzed for long-run
steady-state behavior .

Question 4
TRUE or FALSE? The main method of attack for terminating simulations is via
independent replications.

 A. True
 B. False

Correct Answer: A
Explanation: Independent replications help mitigate issues with simulation outputs not
being i.i.d., providing valid confidence intervals .

Question 5
TRUE or FALSE? Suppose that X₁, X₂, ..., Xₙ are consecutive waiting times, and we define
the sample mean X̄ = ∑Xᵢ/n. Then Var(X̄) = Var(Xᵢ)/n.

 A. True
 B. False

Correct Answer: B
Explanation: Very FALSE! Correlation between observations messes up the variance of
the sample mean. This is one of the main reasons why output analysis is difficult .

Question 6
How can we deal with initialization bias if we want to do a steady-state analysis?

 A. Make an extremely long run to overwhelm it
 B. Truncate (delete) some of the initial data
 C. Use independent replications
 D. Both A and B

, Correct Answer: D
Explanation: Both making a long run to overwhelm the bias and truncating initial data
are valid approaches to handle initialization bias .

Question 7
Suppose that estimator A has bias = 3 and variance = 12, while estimator B has bias = -2
and variance = 14. Which estimator has the lower mean squared error (MSE)?

 A. Estimator A
 B. Estimator B
 C. Both have the same MSE
 D. Cannot be determined

Correct Answer: B
Explanation: MSE = Bias² + Variance. MSE(A) = 9 + 12 = 21. MSE(B) = 4 + 14 = 18.
Estimator B has the lower MSE .

Question 8
If the expected value of your estimator equals the parameter you're trying to estimate,
then your estimator is:

 A. Unbiased
 B. Consistent
 C. Efficient
 D. Sufficient

Correct Answer: A
Explanation: This is the definition of an unbiased estimator .

Question 9
Suppose that X₁, X₂, ..., Xₙ are i.i.d. with mean μ. The sample mean X̄ is:

 A. Unbiased for μ
 B. Biased for μ
 C. Consistent but biased
 D. Neither consistent nor unbiased

Correct Answer: A
Explanation: E[X̄] = μ, so the sample mean is unbiased for the population mean .

, Question 10
Suppose X₁=4, X₂=3, X₃=5 are i.i.d. realizations from an Exp(λ) distribution. What is the
MLE of λ?

 A. 4
 B. 3
 C. 0.25
 D. 0.33

Correct Answer: C
Explanation: For Exp(λ), the MLE of λ is 1/X̄. X̄ = (4+3+5)/3 = 4. So λ̂ = 1/4 = 0.25 .

Question 11
If X₁=2, X₂=-2, and X₃=0 are i.i.d. realizations from a Nor(μ, σ²) distribution, what is the
MLE for the variance σ²?

 A. 4
 B. 2
 C. 8/3
 D. 3

Correct Answer: C
Explanation: The MLE of σ² is ∑(Xᵢ - μ̂)²/n. μ̂ = X̄ = 0. So σ̂² = (4+4+0)/3 = 8/3 .

Question 12
Suppose we observe Poisson(λ) realizations X₁=5, X₂=3, and X₃=1. What is the MLE of λ?

 A. 5
 B. 1
 C. 3
 D. 9

Correct Answer: C
Explanation: For Poisson(λ), the MLE of λ is the sample mean X̄ = (5+3+1)/3 = 3 .




Section 2: Goodness-of-Fit and Hypothesis Testing
Question 13
Suppose we're conducting a χ² goodness-of-fit test with α = 0.01 to determine whether