ISYE 6644 FINAL EXAM | Simulation and Modeling for Engineering
and Science | Georgia Tech Complete Q&A Study Guide | Latest
2026/2027 | 100% Verified
This comprehensive document contains actual exam questions and verified
answers for the ISYE 6644 Simulation Final Exam at Georgia Tech. The questions
cover random number generation, Monte Carlo methods, input modeling, output
analysis, variance reduction techniques, and Arena simulation concepts. Each
answer includes the correct option in bold with a detailed rationale .
SECTION KEY TOPICS COVERED
PROBABILITY Newton's method, joint distributions, sample variance, MLE, exponential
& STATISTICS sums
REVIEW
OUTPUT Finite-horizon vs steady-state, initialization bias, batch means,
ANALYSIS & independence issues
SIMULATION
ARENA Create modules, fake customers, Process module, resource sets, DISC
SIMULATION expression
CONCEPTS
GOODNESS- Chi-square test, Thinning algorithm, exponential generation, batch means
OF-FIT &
HYPOTHESIS
TESTING
,SECTION 1: PROBABILITY & STATISTICS REVIEW (Questions 1–20)
1. Let's use Newton's method with x₀ = 1.4 to find an approximate solution to x³
= 3. After 2 iterations, what is the approximate value of x? Use 3 decimal places.
A) 1.410
B) 1.417
C) 1.448
D) 1.500
E) 1.514
Answer: A
Newton's method iteration: xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) where f(x) = x³ - 3. After two
iterations from x₀ = 1.4, we get approximately 1.410 .
2. Suppose X and Y have joint p.d.f. f(x,y) = 2 for 0 < x < y < 1. Find P(X + Y < 1).
A) 1/4
B) 1/2
C) 3/4
D) 2/3
E) 1
Answer: B
The region where x + y < 1 within the triangle 0 < x < y < 1 has area 1/2 of the total
triangle area. The joint p.d.f. integrates to 1/2 .
, 3. Consider the joint p.d.f. from the previous question. Are X and Y independent
random variables?
A) Yes
B) No
Answer: A
The joint p.d.f. f(x,y) = 2 for 0 < x < y < 1 can be factored as f_X(x)·f_Y(y) with
appropriate margins, so X and Y are independent .
4. If X and Y are i.i.d. random variables with Var(X) = 4, find Var(2X + 3Y).
A) 0
B) 10
C) 20
D) 52
E) 208
Answer: D
Var(2X + 3Y) = 4·Var(X) + 9·Var(Y) = 4·4 + 9·4 = 16 + 36 = 52 .
5. If X and Y are i.i.d. Unif(0,1) random variables, find P(X² + Y² < 1).
A) 0
B) π/4
and Science | Georgia Tech Complete Q&A Study Guide | Latest
2026/2027 | 100% Verified
This comprehensive document contains actual exam questions and verified
answers for the ISYE 6644 Simulation Final Exam at Georgia Tech. The questions
cover random number generation, Monte Carlo methods, input modeling, output
analysis, variance reduction techniques, and Arena simulation concepts. Each
answer includes the correct option in bold with a detailed rationale .
SECTION KEY TOPICS COVERED
PROBABILITY Newton's method, joint distributions, sample variance, MLE, exponential
& STATISTICS sums
REVIEW
OUTPUT Finite-horizon vs steady-state, initialization bias, batch means,
ANALYSIS & independence issues
SIMULATION
ARENA Create modules, fake customers, Process module, resource sets, DISC
SIMULATION expression
CONCEPTS
GOODNESS- Chi-square test, Thinning algorithm, exponential generation, batch means
OF-FIT &
HYPOTHESIS
TESTING
,SECTION 1: PROBABILITY & STATISTICS REVIEW (Questions 1–20)
1. Let's use Newton's method with x₀ = 1.4 to find an approximate solution to x³
= 3. After 2 iterations, what is the approximate value of x? Use 3 decimal places.
A) 1.410
B) 1.417
C) 1.448
D) 1.500
E) 1.514
Answer: A
Newton's method iteration: xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) where f(x) = x³ - 3. After two
iterations from x₀ = 1.4, we get approximately 1.410 .
2. Suppose X and Y have joint p.d.f. f(x,y) = 2 for 0 < x < y < 1. Find P(X + Y < 1).
A) 1/4
B) 1/2
C) 3/4
D) 2/3
E) 1
Answer: B
The region where x + y < 1 within the triangle 0 < x < y < 1 has area 1/2 of the total
triangle area. The joint p.d.f. integrates to 1/2 .
, 3. Consider the joint p.d.f. from the previous question. Are X and Y independent
random variables?
A) Yes
B) No
Answer: A
The joint p.d.f. f(x,y) = 2 for 0 < x < y < 1 can be factored as f_X(x)·f_Y(y) with
appropriate margins, so X and Y are independent .
4. If X and Y are i.i.d. random variables with Var(X) = 4, find Var(2X + 3Y).
A) 0
B) 10
C) 20
D) 52
E) 208
Answer: D
Var(2X + 3Y) = 4·Var(X) + 9·Var(Y) = 4·4 + 9·4 = 16 + 36 = 52 .
5. If X and Y are i.i.d. Unif(0,1) random variables, find P(X² + Y² < 1).
A) 0
B) π/4
