Georgia Tech ISYE 6644 Simulation and Modeling for
Engineering and Science: Exam 1 - Questions with Correct
Answers
100 questions
1. Model calibration means:
A. Generating uniform random numbers
B. Running only one replication
C. Adjusting model parameters so model output agrees with real-system data
D. Removing all randomness
Correct Answer: C. Adjusting model parameters so model output agrees with real-system
data
Rationale: Iterative with validation.
2. For an M/M/1 queue, the expected number in system L equals:
A. rho^2/(1 - rho)
B. 1/(mu - lambda) squared
C. lambda times mu
D. rho/(1 - rho)
Correct Answer: D. rho/(1 - rho)
Rationale: Steady state.
3. A simulation model's level of detail should be:
A. Enough to answer the study questions, no more
B. As much as possible always
C. As little as possible regardless of questions
D. Determined by the random number generator
Correct Answer: A. Enough to answer the study questions, no more
Rationale: Avoid over-modeling.
4. Verification of a simulation model asks:
A. Does the model represent the real system accurately?
B. Is the data normal?
C. Is the computer program implementing the model correctly (built the model right)?
D. Are the random numbers uniform?
Correct Answer: C. Is the computer program implementing the model correctly (built the
model right)?
Rationale: Debugging.
5. Little's Law states that:
A. L = lambda W (average number in system equals arrival rate times average time in system)
B. L = W / lambda
C. L = lambda + W
D. L = mu / lambda
Correct Answer: A. L = lambda W (average number in system equals arrival rate times
average time in system)
Rationale: Holds broadly in steady state.
,6. A simulation 'state' variable is:
A. A variable describing the system at a point in time, such as number in queue
B. A random seed
C. A distribution name
D. A plot
Correct Answer: A. A variable describing the system at a point in time, such as number in
queue
Rationale: State changes at events.
7. An attribute is:
A. A global variable shared by all entities
B. A characteristic attached to an individual entity, such as its arrival time or priority
C. A type of queue
D. A resource capacity
Correct Answer: B. A characteristic attached to an individual entity, such as its arrival time or
priority
Rationale: Local to each entity.
8. Animation in simulation software primarily helps with:
A. Statistical proof of correctness
B. Communication, verification and face validity
C. Generating random numbers
D. Replacing output analysis
Correct Answer: B. Communication, verification and face validity
Rationale: Not a substitute for statistics.
9. A critical point of f(x) occurs where:
A. f'(x) = 0 or f'(x) is undefined
B. f(x) = 0
C. f''(x) = 1
D. x = 0 always
Correct Answer: A. f'(x) = 0 or f'(x) is undefined
Rationale: Candidate extrema.
10. The derivative of sin(x) is:
A. -cos(x)
B. -sin(x)
C. tan(x)
D. cos(x)
Correct Answer: D. cos(x)
Rationale: Basic trig.
11. The mean value theorem guarantees that for a differentiable f on [a, b] there is a c with:
A. f(c) = 0
B. f'(c) = (f(b) - f(a))/(b - a)
C. f''(c) = 0
D. f'(c) = 1
Correct Answer: B. f'(c) = (f(b) - f(a))/(b - a)
Rationale: Average slope.
, 12. An improper integral is one where:
A. A limit of integration is infinite or the integrand is unbounded
B. The integrand is a polynomial
C. The interval is [0, 1]
D. The function is continuous everywhere
Correct Answer: A. A limit of integration is infinite or the integrand is unbounded
Rationale: Evaluate with limits.
13. The binomial theorem gives (x + y)^n as:
A. x^n + y^n
B. The sum over k of C(n, k) x^k y^(n-k)
C. n(x + y)
D. (x y)^n
Correct Answer: B. The sum over k of C(n, k) x^k y^(n-k)
Rationale: Binomial coefficients.
14. A double integral of f(x, y) over a region gives:
A. The slope of f
B. The volume under the surface over that region
C. The arc length
D. The derivative of f
Correct Answer: B. The volume under the surface over that region
Rationale: Used for joint distributions.
15. The Fundamental Theorem of Calculus links:
A. Limits and series only
B. Probability and statistics
C. Differentiation and integration as inverse operations
D. Algebra and geometry
Correct Answer: C. Differentiation and integration as inverse operations
Rationale: F' = f.
16. The integral of x e^(-x) from 0 to infinity equals:
A. 0
B. 2
C. 1
D. 1/2
Correct Answer: C. 1
Rationale: Gamma(2) = 1! = 1.
17. A Poisson(lambda) random variable has mean and variance:
A. lambda and lambda^2
B. 1/lambda and 1/lambda^2
C. lambda and 1
D. Both lambda
Correct Answer: D. Both lambda
Rationale: Equal mean and variance.
Engineering and Science: Exam 1 - Questions with Correct
Answers
100 questions
1. Model calibration means:
A. Generating uniform random numbers
B. Running only one replication
C. Adjusting model parameters so model output agrees with real-system data
D. Removing all randomness
Correct Answer: C. Adjusting model parameters so model output agrees with real-system
data
Rationale: Iterative with validation.
2. For an M/M/1 queue, the expected number in system L equals:
A. rho^2/(1 - rho)
B. 1/(mu - lambda) squared
C. lambda times mu
D. rho/(1 - rho)
Correct Answer: D. rho/(1 - rho)
Rationale: Steady state.
3. A simulation model's level of detail should be:
A. Enough to answer the study questions, no more
B. As much as possible always
C. As little as possible regardless of questions
D. Determined by the random number generator
Correct Answer: A. Enough to answer the study questions, no more
Rationale: Avoid over-modeling.
4. Verification of a simulation model asks:
A. Does the model represent the real system accurately?
B. Is the data normal?
C. Is the computer program implementing the model correctly (built the model right)?
D. Are the random numbers uniform?
Correct Answer: C. Is the computer program implementing the model correctly (built the
model right)?
Rationale: Debugging.
5. Little's Law states that:
A. L = lambda W (average number in system equals arrival rate times average time in system)
B. L = W / lambda
C. L = lambda + W
D. L = mu / lambda
Correct Answer: A. L = lambda W (average number in system equals arrival rate times
average time in system)
Rationale: Holds broadly in steady state.
,6. A simulation 'state' variable is:
A. A variable describing the system at a point in time, such as number in queue
B. A random seed
C. A distribution name
D. A plot
Correct Answer: A. A variable describing the system at a point in time, such as number in
queue
Rationale: State changes at events.
7. An attribute is:
A. A global variable shared by all entities
B. A characteristic attached to an individual entity, such as its arrival time or priority
C. A type of queue
D. A resource capacity
Correct Answer: B. A characteristic attached to an individual entity, such as its arrival time or
priority
Rationale: Local to each entity.
8. Animation in simulation software primarily helps with:
A. Statistical proof of correctness
B. Communication, verification and face validity
C. Generating random numbers
D. Replacing output analysis
Correct Answer: B. Communication, verification and face validity
Rationale: Not a substitute for statistics.
9. A critical point of f(x) occurs where:
A. f'(x) = 0 or f'(x) is undefined
B. f(x) = 0
C. f''(x) = 1
D. x = 0 always
Correct Answer: A. f'(x) = 0 or f'(x) is undefined
Rationale: Candidate extrema.
10. The derivative of sin(x) is:
A. -cos(x)
B. -sin(x)
C. tan(x)
D. cos(x)
Correct Answer: D. cos(x)
Rationale: Basic trig.
11. The mean value theorem guarantees that for a differentiable f on [a, b] there is a c with:
A. f(c) = 0
B. f'(c) = (f(b) - f(a))/(b - a)
C. f''(c) = 0
D. f'(c) = 1
Correct Answer: B. f'(c) = (f(b) - f(a))/(b - a)
Rationale: Average slope.
, 12. An improper integral is one where:
A. A limit of integration is infinite or the integrand is unbounded
B. The integrand is a polynomial
C. The interval is [0, 1]
D. The function is continuous everywhere
Correct Answer: A. A limit of integration is infinite or the integrand is unbounded
Rationale: Evaluate with limits.
13. The binomial theorem gives (x + y)^n as:
A. x^n + y^n
B. The sum over k of C(n, k) x^k y^(n-k)
C. n(x + y)
D. (x y)^n
Correct Answer: B. The sum over k of C(n, k) x^k y^(n-k)
Rationale: Binomial coefficients.
14. A double integral of f(x, y) over a region gives:
A. The slope of f
B. The volume under the surface over that region
C. The arc length
D. The derivative of f
Correct Answer: B. The volume under the surface over that region
Rationale: Used for joint distributions.
15. The Fundamental Theorem of Calculus links:
A. Limits and series only
B. Probability and statistics
C. Differentiation and integration as inverse operations
D. Algebra and geometry
Correct Answer: C. Differentiation and integration as inverse operations
Rationale: F' = f.
16. The integral of x e^(-x) from 0 to infinity equals:
A. 0
B. 2
C. 1
D. 1/2
Correct Answer: C. 1
Rationale: Gamma(2) = 1! = 1.
17. A Poisson(lambda) random variable has mean and variance:
A. lambda and lambda^2
B. 1/lambda and 1/lambda^2
C. lambda and 1
D. Both lambda
Correct Answer: D. Both lambda
Rationale: Equal mean and variance.
