Georgia Tech ISYE 6644 Simulation and Modeling for
Engineering and Science: Exam 2 - Questions with Correct
Answers
100 questions
1. A disadvantage of simulation is that:
A. It cannot handle randomness
B. It only works for continuous systems
C. It never requires data
D. Model building and output interpretation can be time-consuming and require expertise
Correct Answer: D. Model building and output interpretation can be time-consuming and
require expertise
Rationale: Also outputs are random estimates.
2. In Kendall notation, the 'D' in M/D/1 denotes:
A. Discrete uniform service
B. Deterministic (constant) service times
C. Dependent service
D. Delay distribution
Correct Answer: B. Deterministic (constant) service times
Rationale: Constant service.
3. A replication of a simulation is:
A. A run with identical random numbers
B. One event
C. A single customer
D. An independent run using different random numbers with the same initial conditions
Correct Answer: D. An independent run using different random numbers with the same initial
conditions
Rationale: IID outputs across replications.
4. A continuous simulation model typically involves:
A. State variables that change continuously, often via differential equations
B. Only counts of customers
C. Only random number tests
D. Only queue disciplines
Correct Answer: A. State variables that change continuously, often via differential equations
Rationale: e.g., fluid levels, population models.
5. Buffon's needle experiment can be used to estimate:
A. e
B. The golden ratio
C. Pi
D. The square root of 2 only
Correct Answer: C. Pi
Rationale: Needle crossing probability 2L/(pi d).
,6. An event in discrete-event simulation is:
A. A long process taking time
B. A random number stream
C. A statistical estimator
D. An instantaneous occurrence that may change the system state
Correct Answer: D. An instantaneous occurrence that may change the system state
Rationale: e.g., arrival, service completion.
7. For an M/M/1 queue with lambda = 4 and mu = 5 per hour, W equals:
A. 0.8 hours
B. 1 hour
C. 4 hours
D. 0.2 hours
Correct Answer: B. 1 hour
Rationale: 1/(5 - 4).
8. In Kendall notation, M/M/1 means:
A. Exponential interarrivals, exponential service, one server
B. Mixed arrivals, mixed service, one queue
C. Markov arrivals, many servers, one queue
D. Deterministic arrivals and service
Correct Answer: A. Exponential interarrivals, exponential service, one server
Rationale: M = Markovian.
9. The sum of k^2 for k = 1 to n equals:
A. n(n + 1)/2
B. n^3/3 exactly
C. n(n + 1)(2n + 1)/6
D. n^2(n + 1)^2/4
Correct Answer: C. n(n + 1)(2n + 1)/6
Rationale: Sum of squares.
10. C(n, k), the number of combinations, equals:
A. n!/(k!(n - k)!)
B. n!/k!
C. n^k
D. k!/(n - k)!
Correct Answer: A. n!/(k!(n - k)!)
Rationale: Choose.
11. The integral of a constant c from a to b equals:
A. c(b - a)
B. c
C. b - a
D. c/(b - a)
Correct Answer: A. c(b - a)
Rationale: Rectangle.
, 12. The trapezoid rule approximates an integral by:
A. Using random points
B. Taking the derivative
C. Using only the endpoint values multiplied
D. Summing areas of trapezoids under the curve
Correct Answer: D. Summing areas of trapezoids under the curve
Rationale: Numerical integration.
13. Using the trapezoid rule with one interval on f(x) = x^2 over [0, 1] gives:
A. 0.333
B. 1
C. 0.5
D. 0.25
Correct Answer: C. 0.5
Rationale: (1/2)(0 + 1).
14. L'Hopital's rule applies to limits of the form:
A. 1/0 only
B. Any finite ratio
C. 0 times 0
D. 0/0 or infinity/infinity
Correct Answer: D. 0/0 or infinity/infinity
Rationale: Differentiate numerator and denominator.
15. The partial derivative of f(x, y) = x^2 y with respect to x is:
A. x^2
B. 2xy
C. 2x
D. y
Correct Answer: B. 2xy
Rationale: Treat y as constant.
16. The integral of 1/x dx is:
A. x^2/2 + C
B. -1/x^2 + C
C. e^x + C
D. ln|x| + C
Correct Answer: D. ln|x| + C
Rationale: Antiderivative.
17. The memoryless property of the exponential states that:
A. P(X > s + t) = P(X > s) + P(X > t)
B. E[X] = Var(X)
C. P(X > s + t | X > s) = P(X > t)
D. X is always integer-valued
Correct Answer: C. P(X > s + t | X > s) = P(X > t)
Rationale: Only continuous memoryless distribution.
Engineering and Science: Exam 2 - Questions with Correct
Answers
100 questions
1. A disadvantage of simulation is that:
A. It cannot handle randomness
B. It only works for continuous systems
C. It never requires data
D. Model building and output interpretation can be time-consuming and require expertise
Correct Answer: D. Model building and output interpretation can be time-consuming and
require expertise
Rationale: Also outputs are random estimates.
2. In Kendall notation, the 'D' in M/D/1 denotes:
A. Discrete uniform service
B. Deterministic (constant) service times
C. Dependent service
D. Delay distribution
Correct Answer: B. Deterministic (constant) service times
Rationale: Constant service.
3. A replication of a simulation is:
A. A run with identical random numbers
B. One event
C. A single customer
D. An independent run using different random numbers with the same initial conditions
Correct Answer: D. An independent run using different random numbers with the same initial
conditions
Rationale: IID outputs across replications.
4. A continuous simulation model typically involves:
A. State variables that change continuously, often via differential equations
B. Only counts of customers
C. Only random number tests
D. Only queue disciplines
Correct Answer: A. State variables that change continuously, often via differential equations
Rationale: e.g., fluid levels, population models.
5. Buffon's needle experiment can be used to estimate:
A. e
B. The golden ratio
C. Pi
D. The square root of 2 only
Correct Answer: C. Pi
Rationale: Needle crossing probability 2L/(pi d).
,6. An event in discrete-event simulation is:
A. A long process taking time
B. A random number stream
C. A statistical estimator
D. An instantaneous occurrence that may change the system state
Correct Answer: D. An instantaneous occurrence that may change the system state
Rationale: e.g., arrival, service completion.
7. For an M/M/1 queue with lambda = 4 and mu = 5 per hour, W equals:
A. 0.8 hours
B. 1 hour
C. 4 hours
D. 0.2 hours
Correct Answer: B. 1 hour
Rationale: 1/(5 - 4).
8. In Kendall notation, M/M/1 means:
A. Exponential interarrivals, exponential service, one server
B. Mixed arrivals, mixed service, one queue
C. Markov arrivals, many servers, one queue
D. Deterministic arrivals and service
Correct Answer: A. Exponential interarrivals, exponential service, one server
Rationale: M = Markovian.
9. The sum of k^2 for k = 1 to n equals:
A. n(n + 1)/2
B. n^3/3 exactly
C. n(n + 1)(2n + 1)/6
D. n^2(n + 1)^2/4
Correct Answer: C. n(n + 1)(2n + 1)/6
Rationale: Sum of squares.
10. C(n, k), the number of combinations, equals:
A. n!/(k!(n - k)!)
B. n!/k!
C. n^k
D. k!/(n - k)!
Correct Answer: A. n!/(k!(n - k)!)
Rationale: Choose.
11. The integral of a constant c from a to b equals:
A. c(b - a)
B. c
C. b - a
D. c/(b - a)
Correct Answer: A. c(b - a)
Rationale: Rectangle.
, 12. The trapezoid rule approximates an integral by:
A. Using random points
B. Taking the derivative
C. Using only the endpoint values multiplied
D. Summing areas of trapezoids under the curve
Correct Answer: D. Summing areas of trapezoids under the curve
Rationale: Numerical integration.
13. Using the trapezoid rule with one interval on f(x) = x^2 over [0, 1] gives:
A. 0.333
B. 1
C. 0.5
D. 0.25
Correct Answer: C. 0.5
Rationale: (1/2)(0 + 1).
14. L'Hopital's rule applies to limits of the form:
A. 1/0 only
B. Any finite ratio
C. 0 times 0
D. 0/0 or infinity/infinity
Correct Answer: D. 0/0 or infinity/infinity
Rationale: Differentiate numerator and denominator.
15. The partial derivative of f(x, y) = x^2 y with respect to x is:
A. x^2
B. 2xy
C. 2x
D. y
Correct Answer: B. 2xy
Rationale: Treat y as constant.
16. The integral of 1/x dx is:
A. x^2/2 + C
B. -1/x^2 + C
C. e^x + C
D. ln|x| + C
Correct Answer: D. ln|x| + C
Rationale: Antiderivative.
17. The memoryless property of the exponential states that:
A. P(X > s + t) = P(X > s) + P(X > t)
B. E[X] = Var(X)
C. P(X > s + t | X > s) = P(X > t)
D. X is always integer-valued
Correct Answer: C. P(X > s + t | X > s) = P(X > t)
Rationale: Only continuous memoryless distribution.
