Georgia Tech ISYE 6644 Simulation and Modeling for
Engineering and Science: Final Exam (Comprehensive) -
Questions with Correct Answers
100 questions
1. The hypergeometric distribution models:
A. Draws with replacement
B. Successes in draws without replacement from a finite population
C. Time between arrivals
D. Continuous measurements
Correct Answer: B. Successes in draws without replacement from a finite population
Rationale: Finite population.
2. The Weibull distribution is commonly used to model:
A. Number of arrivals
B. Coin flips
C. Discrete counts only
D. Time to failure (reliability)
Correct Answer: D. Time to failure (reliability)
Rationale: Flexible hazard.
3. The sample mean X-bar of IID observations with mean mu is:
A. A biased estimator of mu
B. Equal to mu always
C. An unbiased estimator of mu
D. An estimator of variance
Correct Answer: C. An unbiased estimator of mu
Rationale: E[X-bar] = mu.
4. For IID Bernoulli(p) data, the MLE of p is:
A. 1/X-bar
B. The sample proportion of successes
C. The sample variance
D. 0.5 always
Correct Answer: B. The sample proportion of successes
Rationale: X-bar.
5. The 'stopping time' of a simulated random walk refers to:
A. The total CPU time
B. The warm-up period
C. The end of the RNG cycle
D. The first time it hits a specified boundary
Correct Answer: D. The first time it hits a specified boundary
Rationale: Gambler's ruin.
,6. The 'hit-or-miss' Monte Carlo method estimates an integral by:
A. The proportion of random points under the curve times the bounding box area
B. Averaging function values
C. Using the trapezoid rule
D. Solving a differential equation
Correct Answer: A. The proportion of random points under the curve times the bounding box
area
Rationale: Usually less efficient than sample-mean MC.
7. The cost of a simulation study is often driven mostly by:
A. Computer hardware
B. Software license only
C. Random number generation
D. Data collection and model development time
Correct Answer: D. Data collection and model development time
Rationale: People time.
8. Combined discrete-continuous simulation is useful when:
A. There is no time
B. Only Monte Carlo is needed
C. Some state variables change continuously and others at discrete events
D. No randomness exists
Correct Answer: C. Some state variables change continuously and others at discrete events
Rationale: e.g., tank levels with discrete valves.
9. In Arena, the variable NQ(Queue Name) returns:
A. The queue's capacity
B. The current number of entities in that queue
C. The total arrivals
D. The average wait
Correct Answer: B. The current number of entities in that queue
Rationale: Built-in variable.
10. When a resource's capacity decreases while busy, Arena's 'Ignore' rule:
A. Preempts the entity immediately
B. Waits until all work is done
C. Cancels the schedule
D. Lets the current service finish, then reduces capacity
Correct Answer: D. Lets the current service finish, then reduces capacity
Rationale: Also Wait and Preempt.
11. To implement a(X) mod m without overflow on 32-bit machines, one may use:
A. Schrage's method (approximate factorization)
B. Floating-point rounding only
C. Middle-square
D. Box-Muller
Correct Answer: A. Schrage's method (approximate factorization)
Rationale: Portable implementation.
, 12. Fibonacci generators X_i = (X_(i-1) + X_(i-2)) mod m have:
A. Perfect independence
B. Poor statistical properties in simple form
C. Infinite period
D. No periodicity
Correct Answer: B. Poor statistical properties in simple form
Rationale: Lagged versions improved.
13. A generator's period is:
A. The time to generate one number
B. The number of values before the sequence repeats
C. The seed
D. The modulus divided by 2
Correct Answer: B. The number of values before the sequence repeats
Rationale: Cycle length.
14. A runs test is used to test:
A. Uniformity only
B. Normality
C. Independence of the sequence
D. Equality of variances
Correct Answer: C. Independence of the sequence
Rationale: Too many or too few runs signal dependence.
15. A rule of thumb for the chi-square test is that each expected count should be at least:
A. 5
B. 1
C. 100
D. 50
Correct Answer: A. 5
Rationale: Approximation validity.
16. The chi-square test statistic is:
A. The sum of (O_i - E_i)
B. The maximum |O_i - E_i|
C. The sum of O_i E_i
D. The sum of (O_i - E_i)^2/E_i
Correct Answer: D. The sum of (O_i - E_i)^2/E_i
Rationale: Approximately chi-square with k - 1 df.
17. The chi-square test for uniformity divides (0, 1) into k cells and compares:
A. Means only
B. Variances only
C. Observed counts with expected counts n/k
D. Runs up and down
Correct Answer: C. Observed counts with expected counts n/k
Rationale: Goodness of fit.
Engineering and Science: Final Exam (Comprehensive) -
Questions with Correct Answers
100 questions
1. The hypergeometric distribution models:
A. Draws with replacement
B. Successes in draws without replacement from a finite population
C. Time between arrivals
D. Continuous measurements
Correct Answer: B. Successes in draws without replacement from a finite population
Rationale: Finite population.
2. The Weibull distribution is commonly used to model:
A. Number of arrivals
B. Coin flips
C. Discrete counts only
D. Time to failure (reliability)
Correct Answer: D. Time to failure (reliability)
Rationale: Flexible hazard.
3. The sample mean X-bar of IID observations with mean mu is:
A. A biased estimator of mu
B. Equal to mu always
C. An unbiased estimator of mu
D. An estimator of variance
Correct Answer: C. An unbiased estimator of mu
Rationale: E[X-bar] = mu.
4. For IID Bernoulli(p) data, the MLE of p is:
A. 1/X-bar
B. The sample proportion of successes
C. The sample variance
D. 0.5 always
Correct Answer: B. The sample proportion of successes
Rationale: X-bar.
5. The 'stopping time' of a simulated random walk refers to:
A. The total CPU time
B. The warm-up period
C. The end of the RNG cycle
D. The first time it hits a specified boundary
Correct Answer: D. The first time it hits a specified boundary
Rationale: Gambler's ruin.
,6. The 'hit-or-miss' Monte Carlo method estimates an integral by:
A. The proportion of random points under the curve times the bounding box area
B. Averaging function values
C. Using the trapezoid rule
D. Solving a differential equation
Correct Answer: A. The proportion of random points under the curve times the bounding box
area
Rationale: Usually less efficient than sample-mean MC.
7. The cost of a simulation study is often driven mostly by:
A. Computer hardware
B. Software license only
C. Random number generation
D. Data collection and model development time
Correct Answer: D. Data collection and model development time
Rationale: People time.
8. Combined discrete-continuous simulation is useful when:
A. There is no time
B. Only Monte Carlo is needed
C. Some state variables change continuously and others at discrete events
D. No randomness exists
Correct Answer: C. Some state variables change continuously and others at discrete events
Rationale: e.g., tank levels with discrete valves.
9. In Arena, the variable NQ(Queue Name) returns:
A. The queue's capacity
B. The current number of entities in that queue
C. The total arrivals
D. The average wait
Correct Answer: B. The current number of entities in that queue
Rationale: Built-in variable.
10. When a resource's capacity decreases while busy, Arena's 'Ignore' rule:
A. Preempts the entity immediately
B. Waits until all work is done
C. Cancels the schedule
D. Lets the current service finish, then reduces capacity
Correct Answer: D. Lets the current service finish, then reduces capacity
Rationale: Also Wait and Preempt.
11. To implement a(X) mod m without overflow on 32-bit machines, one may use:
A. Schrage's method (approximate factorization)
B. Floating-point rounding only
C. Middle-square
D. Box-Muller
Correct Answer: A. Schrage's method (approximate factorization)
Rationale: Portable implementation.
, 12. Fibonacci generators X_i = (X_(i-1) + X_(i-2)) mod m have:
A. Perfect independence
B. Poor statistical properties in simple form
C. Infinite period
D. No periodicity
Correct Answer: B. Poor statistical properties in simple form
Rationale: Lagged versions improved.
13. A generator's period is:
A. The time to generate one number
B. The number of values before the sequence repeats
C. The seed
D. The modulus divided by 2
Correct Answer: B. The number of values before the sequence repeats
Rationale: Cycle length.
14. A runs test is used to test:
A. Uniformity only
B. Normality
C. Independence of the sequence
D. Equality of variances
Correct Answer: C. Independence of the sequence
Rationale: Too many or too few runs signal dependence.
15. A rule of thumb for the chi-square test is that each expected count should be at least:
A. 5
B. 1
C. 100
D. 50
Correct Answer: A. 5
Rationale: Approximation validity.
16. The chi-square test statistic is:
A. The sum of (O_i - E_i)
B. The maximum |O_i - E_i|
C. The sum of O_i E_i
D. The sum of (O_i - E_i)^2/E_i
Correct Answer: D. The sum of (O_i - E_i)^2/E_i
Rationale: Approximately chi-square with k - 1 df.
17. The chi-square test for uniformity divides (0, 1) into k cells and compares:
A. Means only
B. Variances only
C. Observed counts with expected counts n/k
D. Runs up and down
Correct Answer: C. Observed counts with expected counts n/k
Rationale: Goodness of fit.
