ISYE 6644 Exam 3 Practice Questions – Spring
2026 Complete Study Guide with Verified
Questions, Answers & Rationales Georgia
Institute of Technology
Core Domains Covered
• Input Modeling & Goodness-of-Fit – Distribution selection, parameter
estimation (MLE, MoM), Kolmogorov-Smirnov test, chi-square test,
Anderson-Darling test, Q-Q plots, P-P plots
• Output Analysis – Confidence intervals, batch means, independent
replications, steady-state vs. terminating simulations, initialization bias,
Welch's method, sample size determination
• Variance Reduction Techniques – Common random numbers (CRN),
antithetic variates, control variates, importance sampling, stratified
sampling
• Simulation Optimization & Ranking/Selection – Response surface
methodology, metamodeling, gradient estimation, indifference-zone
methods, multiple comparisons
• Random Number & Variate Generation – Linear congruential
generators, inverse transform method, acceptance-rejection method,
composition method, properties of random number generators
• Experimental Design – Factorial designs, fractional factorial designs,
screening experiments, response surface designs
• Verification & Validation – Model verification, face validity, sensitivity
analysis, validation techniques
• Advanced Topics – Stochastic processes, queueing theory, Markov
chains, Brownian motion, discrete-event simulation fundamentals
,SECTION 1: INPUT MODELING & GOODNESS-OF-FIT (Questions 1–30)
1. You have collected 100 data points and want to fit a distribution. The
Kolmogorov-Smirnov test statistic Dₙ is calculated as 0.15. The critical
value at α = 0.05 for n = 100 is approximately 1.36/√n = 0.136. What is
the correct interpretation?
A. Fail to reject H₀; the fitted distribution is adequate
B. Reject H₀; the fitted distribution is not a good fit
C. The test is inconclusive
D. Accept H₀ with 95% confidence
Rationale: Since the test statistic Dₙ = 0.15 exceeds the critical value 0.136,
we reject the null hypothesis that the data come from the fitted distribution.
This indicates a poor fit at the 5% significance level.
2. Which goodness-of-fit test is most appropriate for testing uniformity
of pseudo-random numbers when the parameters are estimated from
the data?
A. Kolmogorov-Smirnov test
B. Chi-square test
C. Anderson-Darling test
D. Shapiro-Wilk test
Rationale: The chi-square goodness-of-fit test is preferred when parameters
are estimated because it naturally accounts for the reduction in degrees of
freedom. The Kolmogorov-Smirnov test is designed for fully specified
distributions with known parameters.
3. TRUE or FALSE? In a chi-square goodness-of-fit test with 5 intervals
and 2 estimated parameters, the degrees of freedom are 5 − 1 − 2 = 2.
A. True
B. False
,Rationale: For the chi-square goodness-of-fit test, degrees of freedom = k − 1
− s, where k is the number of intervals and s is the number of estimated
parameters. With k = 5 and s = 2, df = 2.
4. For the lognormal distribution with parameters μ and σ², what is the
method of moments estimator for μ?
A. μ̂ = ln(X̄ )
B. μ̂ = ln(X̄ ) − ½σ̂ ²
C. μ̂ = X̄
D. μ̂ = ln(X̄ ²)
Rationale: For the lognormal distribution, E[X] = e^(μ + σ²/2). Taking logs
gives μ = ln(E[X]) − σ²/2. Thus the MoM estimator is μ̂ = ln(X̄ ) − ½σ̂ ².
5. A Q-Q plot is used to:
A. Estimate the parameters of a distribution
B. Assess how well a theoretical distribution fits the sample data
C. Test for independence of observations
D. Determine the sample size needed for a simulation
Rationale: A Q-Q (quantile-quantile) plot compares the quantiles of the
sample data to the quantiles of a theoretical distribution. If the points fall
approximately on a straight line, the fit is good.
6. Which of the following is NOT a step in the input modeling process?
A. Collecting data from the real system
B. Identifying a distribution family
C. Estimating parameters of the chosen distribution
D. Running the simulation model
Rationale: Input modeling involves collecting data, identifying a distribution,
estimating parameters, and validating the fit. Running the simulation is a
separate step that occurs after input modeling is complete.
, 7. The Anderson-Darling test differs from the Kolmogorov-Smirnov test
primarily because:
A. It is a parametric test
B. It gives more weight to the tails of the distribution
C. It requires fewer data points
D. It is only used for normal distributions
Rationale: The Anderson-Darling test is a modification of the Kolmogorov-
Smirnov test that gives more weight to the tails of the distribution, making it
more sensitive to discrepancies in the tails.
8. A simulation analyst has collected 200 observations and wants to fit a
normal distribution. The Shapiro-Wilk test statistic is 0.95 with a p-value
of 0.03. At α = 0.05, what should the analyst conclude?
A. Fail to reject normality; the normal distribution is adequate
B. Reject normality; the normal distribution is not a good fit
C. The test is inconclusive
D. Accept normality with 95% confidence
Rationale: Since the p-value (0.03) is less than α (0.05), we reject the null
hypothesis of normality. The data do not appear to come from a normal
distribution.
9. The method of maximum likelihood estimation (MLE) for distribution
parameters:
A. Always produces unbiased estimators
B. Finds parameter values that maximize the likelihood function
C. Is only applicable to normal distributions
D. Requires less computation than method of moments
Rationale: MLE finds the parameter values that maximize the likelihood
function, which represents the probability of observing the given data. MLE
estimators have desirable asymptotic properties but are not always unbiased.
2026 Complete Study Guide with Verified
Questions, Answers & Rationales Georgia
Institute of Technology
Core Domains Covered
• Input Modeling & Goodness-of-Fit – Distribution selection, parameter
estimation (MLE, MoM), Kolmogorov-Smirnov test, chi-square test,
Anderson-Darling test, Q-Q plots, P-P plots
• Output Analysis – Confidence intervals, batch means, independent
replications, steady-state vs. terminating simulations, initialization bias,
Welch's method, sample size determination
• Variance Reduction Techniques – Common random numbers (CRN),
antithetic variates, control variates, importance sampling, stratified
sampling
• Simulation Optimization & Ranking/Selection – Response surface
methodology, metamodeling, gradient estimation, indifference-zone
methods, multiple comparisons
• Random Number & Variate Generation – Linear congruential
generators, inverse transform method, acceptance-rejection method,
composition method, properties of random number generators
• Experimental Design – Factorial designs, fractional factorial designs,
screening experiments, response surface designs
• Verification & Validation – Model verification, face validity, sensitivity
analysis, validation techniques
• Advanced Topics – Stochastic processes, queueing theory, Markov
chains, Brownian motion, discrete-event simulation fundamentals
,SECTION 1: INPUT MODELING & GOODNESS-OF-FIT (Questions 1–30)
1. You have collected 100 data points and want to fit a distribution. The
Kolmogorov-Smirnov test statistic Dₙ is calculated as 0.15. The critical
value at α = 0.05 for n = 100 is approximately 1.36/√n = 0.136. What is
the correct interpretation?
A. Fail to reject H₀; the fitted distribution is adequate
B. Reject H₀; the fitted distribution is not a good fit
C. The test is inconclusive
D. Accept H₀ with 95% confidence
Rationale: Since the test statistic Dₙ = 0.15 exceeds the critical value 0.136,
we reject the null hypothesis that the data come from the fitted distribution.
This indicates a poor fit at the 5% significance level.
2. Which goodness-of-fit test is most appropriate for testing uniformity
of pseudo-random numbers when the parameters are estimated from
the data?
A. Kolmogorov-Smirnov test
B. Chi-square test
C. Anderson-Darling test
D. Shapiro-Wilk test
Rationale: The chi-square goodness-of-fit test is preferred when parameters
are estimated because it naturally accounts for the reduction in degrees of
freedom. The Kolmogorov-Smirnov test is designed for fully specified
distributions with known parameters.
3. TRUE or FALSE? In a chi-square goodness-of-fit test with 5 intervals
and 2 estimated parameters, the degrees of freedom are 5 − 1 − 2 = 2.
A. True
B. False
,Rationale: For the chi-square goodness-of-fit test, degrees of freedom = k − 1
− s, where k is the number of intervals and s is the number of estimated
parameters. With k = 5 and s = 2, df = 2.
4. For the lognormal distribution with parameters μ and σ², what is the
method of moments estimator for μ?
A. μ̂ = ln(X̄ )
B. μ̂ = ln(X̄ ) − ½σ̂ ²
C. μ̂ = X̄
D. μ̂ = ln(X̄ ²)
Rationale: For the lognormal distribution, E[X] = e^(μ + σ²/2). Taking logs
gives μ = ln(E[X]) − σ²/2. Thus the MoM estimator is μ̂ = ln(X̄ ) − ½σ̂ ².
5. A Q-Q plot is used to:
A. Estimate the parameters of a distribution
B. Assess how well a theoretical distribution fits the sample data
C. Test for independence of observations
D. Determine the sample size needed for a simulation
Rationale: A Q-Q (quantile-quantile) plot compares the quantiles of the
sample data to the quantiles of a theoretical distribution. If the points fall
approximately on a straight line, the fit is good.
6. Which of the following is NOT a step in the input modeling process?
A. Collecting data from the real system
B. Identifying a distribution family
C. Estimating parameters of the chosen distribution
D. Running the simulation model
Rationale: Input modeling involves collecting data, identifying a distribution,
estimating parameters, and validating the fit. Running the simulation is a
separate step that occurs after input modeling is complete.
, 7. The Anderson-Darling test differs from the Kolmogorov-Smirnov test
primarily because:
A. It is a parametric test
B. It gives more weight to the tails of the distribution
C. It requires fewer data points
D. It is only used for normal distributions
Rationale: The Anderson-Darling test is a modification of the Kolmogorov-
Smirnov test that gives more weight to the tails of the distribution, making it
more sensitive to discrepancies in the tails.
8. A simulation analyst has collected 200 observations and wants to fit a
normal distribution. The Shapiro-Wilk test statistic is 0.95 with a p-value
of 0.03. At α = 0.05, what should the analyst conclude?
A. Fail to reject normality; the normal distribution is adequate
B. Reject normality; the normal distribution is not a good fit
C. The test is inconclusive
D. Accept normality with 95% confidence
Rationale: Since the p-value (0.03) is less than α (0.05), we reject the null
hypothesis of normality. The data do not appear to come from a normal
distribution.
9. The method of maximum likelihood estimation (MLE) for distribution
parameters:
A. Always produces unbiased estimators
B. Finds parameter values that maximize the likelihood function
C. Is only applicable to normal distributions
D. Requires less computation than method of moments
Rationale: MLE finds the parameter values that maximize the likelihood
function, which represents the probability of observing the given data. MLE
estimators have desirable asymptotic properties but are not always unbiased.
