Download ISYE 6644 OH Exam 1 Solutions — Spring 2026 Georgia Institute of Technology | Simulation a and more Exams Engineering in PDF only on Docsity!
ISYE 6644 OH Exam 1 Solutions — Spring 2026 Georgia Institute of Technology | Simulation and Modeling for Engineering and Science COURSE OVERVIEW ISYE 6644 — Simulation is a core course in Georgia Tech's OMSA and ISyE programs, covering modeling of discrete-event dynamic systems and simulation-based methods for solving engineering design and analysis problems. Instructor: Dr. David Goldsman EXAM 1 FORMAT & POLICIES
AspectDetails Questions34 questions (33 @ 3 points each; 1 @ 1 point) Total Points100 Time Limit120 minutes Allowed MaterialsOne cheat sheet (both sides) ProctoringRequired Question TypesMultiple choice and True/False
SECTION 1: PROBABILITY & STATISTICS FOUNDATIONS
Question 1: What is the probability of rolling a sum of 7 with two fair six-sided dice?
A) 1/
B) 5/
C) 6/
D) 1/
Correct Answer: C) 6/36 = 1/ Rationale: There are 6 combinations that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) out of 36 total possible outcomes.
Question 2: If P(A) = 0.3, P(B) = 0.4, and A and B are independent, what is P(A ∪ B)? A) 0. B) 0. C) 0. D) 0. Correct Answer: B) 0. Rationale: For independent events, P(A ∩ B) = P(A)P(B) = 0.3 × 0.4 = 0.12. Then P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.3 + 0.4 - 0.12 = 0.58.
Question 5: A random variable with equal mean and variance is most likely which distribution? A) Normal B) Binomial C) Poisson D) Uniform Correct Answer: C) Poisson Rationale: For a Poisson distribution with parameter λ, both the mean and variance are equal to λ.
Question 6: What is the probability that a Poisson(λ=4) random variable equals 3? A) 0. B) 0. C) 0. D) 0. Correct Answer: C) 0. Rationale: P(X = 3) = (e⁻⁴ × 4³) / 3! = (0.0183 × 64) / 6 = 0.1954.
Question 7: TRUE or FALSE: The Central Limit Theorem states that the sum of independent random variables is always normally distributed regardless of sample size. Correct Answer: FALSE Rationale: The CLT states that the sum (or average) of independent random variables approaches a normal distribution as the sample size becomes large (typically n ≥ 30), not for any sample size.
Question 8: What is the expected value of a continuous uniform random variable on [a, b]? A) (a + b) / 2 B) (b - a) / 2 C) (a + b) / 6 D) (b - a) / 12 Correct Answer: A) (a + b) / 2 Rationale: For a uniform distribution U(a,b), E[X] = (a + b)/2 and Var(X) = (b - a)²/12.
Question 9: If X ~ N(μ, σ²), what is the standardized value (z-score) formula?
SECTION 2: SIMULATION FUNDAMENTALS
Question 11: What is a discrete-event simulation? A) A simulation where time advances in fixed increments B) A simulation where the state changes only at discrete points in time C) A simulation that models continuous processes D) A simulation that uses only random numbers Correct Answer: B) A simulation where the state changes only at discrete points in time Rationale: Discrete-event simulation models systems where state changes occur at specific event times, not continuously.
Question 12: TRUE or FALSE: Monte Carlo simulation is a type of discrete-event simulation. Correct Answer: FALSE Rationale: Monte Carlo simulation involves repeated random sampling to obtain numerical results and is typically static (non-time-varying). Discrete-event simulation models dynamic systems with time-sequenced events. They are related but distinct.
Question 13: What is the primary purpose of a simulation study? A) To find the exact optimal solution B) To analyze and understand system behavior C) To replace analytical models D) To eliminate uncertainty Correct Answer: B) To analyze and understand system behavior Rationale: Simulation is used to gain insight into system behavior, evaluate alternatives, and support decision-making.
Question 14: Which of the following is NOT an advantage of simulation? A) Ability to model complex systems B) Allows "what-if" analysis C) Provides optimal solutions D) Can study systems over long time periods Correct Answer: C) Provides optimal solutions Rationale: Simulation provides estimates and insights but does not guarantee optimal solutions. Optimization requires additional techniques.
Question 17: The Linear Congruential Generator (LCG) formula is: A) Xₙ₊₁ = (aXₙ + c) mod m B) Xₙ₊₁ = (aXₙ + c) / m C) Xₙ₊₁ = (a + cXₙ) mod m D) Xₙ₊₁ = (aXₙ - c) mod m Correct Answer: A) Xₙ₊₁ = (aXₙ + c) mod m Rationale: The LCG is the most common pseudo-random number generator: Xₙ₊₁ = (aXₙ + c) mod m.
Question 18: TRUE or FALSE: A random number generator should have a long period. Correct Answer: TRUE Rationale: A long period ensures the sequence does not repeat too quickly, maintaining randomness for large simulations.
Question 19: Which of the following is a desirable property of a random number generator?
A) Uniformity B) Independence C) Reproducibility D) All of the above Correct Answer: D) All of the above Rationale: Good RNGs should produce uniform, independent sequences and be reproducible for verification.
Question 20: The seed of a random number generator determines: A) The distribution of the sequence B) The starting point of the sequence C) The period of the sequence D) The variance of the sequence Correct Answer: B) The starting point of the sequence Rationale: The seed initializes the generator; different seeds produce different sequences.
Rationale: Histograms, probability plots, and goodness-of-fit tests are all used in distribution selection.
Question 23: TRUE or FALSE: The chi-square goodness-of-fit test is used to determine if data comes from a specified distribution. Correct Answer: TRUE Rationale: The chi-square test compares observed frequencies to expected frequencies under a hypothesized distribution.
Question 24: The Kolmogorov-Smirnov test differs from the chi-square test in that: A) It requires larger sample sizes B) It is for continuous distributions C) It uses the cumulative distribution function D) Both B and C Correct Answer: D) Both B and C Rationale: The KS test is for continuous distributions and compares the empirical CDF to the hypothesized CDF.
Question 25: Which parameter is estimated for an exponential distribution? A) Mean μ B) Rate λ C) Standard deviation σ D) Both A and B Correct Answer: D) Both A and B Rationale: For an exponential distribution, rate λ = 1/mean μ.
SECTION 5: OUTPUT ANALYSIS
Question 26: What is the purpose of output analysis in simulation? A) To generate random numbers B) To analyze simulation results and draw conclusions C) To build the simulation model D) To select input distributions
Question 29: What is a confidence interval in simulation? A) A range of values that contains the true parameter with a certain probability B) The range of simulated values C) The standard deviation of the sample D) The sample mean Correct Answer: A) A range of values that contains the true parameter with a certain probability Rationale: Confidence intervals provide a range of plausible values for the true parameter.
Question 30: Which method is used to reduce variance in simulation output? A) Common random numbers B) Antithetic variates C) Control variates D) All of the above Correct Answer: D) All of the above
Rationale: Variance reduction techniques include common random numbers, antithetic variates, and control variates.
SECTION 6: QUEUING THEORY
Question 31: In Kendall notation, M/M/1 represents: A) A single-server queue with exponential interarrival and service times B) A single-server queue with deterministic service times C) A multiple-server queue D) A queue with finite capacity Correct Answer: A) A single-server queue with exponential interarrival and service times Rationale: M/M/1 denotes exponential interarrival times (Markovian), exponential service times, and 1 server.
Question 32: What is traffic intensity ρ in an M/M/1 queue? A) λ / μ B) μ / λ
Rationale: L = ρ/(1-ρ) for an M/M/1 queue.
WHERE TO FIND COMPLETE EXAM SOLUTIONS The complete ISYE 6644 OH Exam 1 Solutions for Spring 2026 are available through the following resources:
ResourceDescription Docsity"ISYE 6644 OH Exam 1 SolutionsQuestions and Answers2026 Update100% Correct.-GT." Stuvia"ISYE- 6644 - ASY, OAN EXAM 1: SIMULATIONQUESTIONS AND ANSWERS2026 UPDATE"
Note: This study guide is based on the Georgia Tech ISYE 6644 course materials and publicly available exam resources for Spring 2026. The complete exam with all 34 questions and solutions can be accessed through the above platforms. For the most accurate and comprehensive preparation, consult the official course materials provided by Dr. David Goldsman and the course website.
