Georgia Tech ISYE 6644 Simulation and Modeling for Engineering and Science: Practice Test 2 (Units 8-13) Questions with Correct Answers

Georgia Tech ISYE 6644 Simulation and Modeling for
Engineering and Science: Practice Test 2 (Units 8-13) -
Questions with Correct Answers
100 questions

1. An LCG with c = 0 is called:
A. A Tausworthe generator
B. A multiplicative (Lehmer) generator
C. A combined generator
D. A Fibonacci generator
Correct Answer: B. A multiplicative (Lehmer) generator
Rationale: Pure multiplicative.

2. The maximum possible period of an LCG with modulus m is:
A. m^2
B. 2^m
C. a
D. m
Correct Answer: D. m
Rationale: Full period.

3. For the LCG X_i = 5 X_(i-1) mod 7 with X_0 = 1, X_2 equals:
A. 4
B. 5
C. 25
D. 3
Correct Answer: A. 4
Rationale: X1 = 5, X2 = 25 mod 7 = 4.

4. For the K-S test with n uniforms, D = max(D+, D-) where D+ is:
A. The maximum of R(i) - i/n
B. The maximum of i/n - R(i)
C. The mean of R(i)
D. The minimum of R(i)
Correct Answer: B. The maximum of i/n - R(i)
Rationale: Order statistics.

5. Desirable properties of a PRN generator include:
A. Short period and slow speed
B. Long period, speed, reproducibility and good statistical properties
C. Unpredictable irreproducible output
D. Only integers
Correct Answer: B. Long period, speed, reproducibility and good statistical properties
Rationale: Requirements.

6. The middle-square method of von Neumann suffers from:
A. Too long a period
B. Perfect randomness
C. Short cycles and degeneration to zero
D. Excessive speed
Correct Answer: C. Short cycles and degeneration to zero
Rationale: Historical.

,7. A generator outputs 0.12, 0.25, 0.37, 0.49, 0.62, 0.74, 0.87 in sequence. This is suspicious
mainly because:
A. The values are not between 0 and 1
B. There are too few decimals
C. The values follow an obvious increasing pattern (not independent)
D. The mean is far from 0.5
Correct Answer: C. The values follow an obvious increasing pattern (not independent)
Rationale: Independence failure; runs test would flag.

8. The uniform output of an LCG is:
A. R_i = X_i/m
B. R_i = X_i times m
C. R_i = a/X_i
D. R_i = X_i mod a
Correct Answer: A. R_i = X_i/m
Rationale: Scale to (0, 1).

9. Combined generators (e.g., L'Ecuyer's MRG32k3a) are used because they:
A. Are simpler than single LCGs
B. Have shorter periods
C. Avoid any recursion
D. Achieve longer periods and better statistical properties
Correct Answer: D. Achieve longer periods and better statistical properties
Rationale: Arena's generator.

10. The LCG X_i = 2 X_(i-1) mod 7 with seed 1 has period:
A. 3
B. 6
C. 7
D. 2
Correct Answer: A. 3
Rationale: 1, 2, 4, 1; 2 is not a primitive root.

11. For an LCG with c > 0 and m = 2^k, full period requires:
A. c even
B. c odd and a - 1 divisible by 4
C. a = 1
D. c = 0
Correct Answer: B. c odd and a - 1 divisible by 4
Rationale: Hull-Dobell theorem.

12. A multiplicative LCG with prime modulus m can achieve period:
A. m
B. m^2
C. m - 1 (when a is a primitive root)
D. 2
Correct Answer: C. m - 1 (when a is a primitive root)
Rationale: Zero excluded.

, 13. RANDU, with X_i = 65539 X_(i-1) mod 2^31, is infamous because:
A. It has period 1
B. Consecutive triples fall on only 15 planes in the unit cube
C. It produces negative numbers
D. It is too slow
Correct Answer: B. Consecutive triples fall on only 15 planes in the unit cube
Rationale: Poor lattice structure.

14. A random number 'stream' is:
A. A physical device
B. A separate subsequence of a generator used for one source of randomness
C. A statistical test
D. An output report
Correct Answer: B. A separate subsequence of a generator used for one source of
randomness
Rationale: Supports CRN.

15. Truly random numbers from physical processes are seldom used in simulation because they
are:
A. Too uniform
B. Not random
C. Not reproducible and slower
D. Free
Correct Answer: C. Not reproducible and slower
Rationale: PRNs preferred.

16. The 'desert island' generator X_i = 16807 X_(i-1) mod (2^31 - 1) is:
A. A Tausworthe generator
B. A combined MRG
C. A truly random generator
D. A well-known multiplicative LCG with period 2^31 - 2
Correct Answer: D. A well-known multiplicative LCG with period 2^31 - 2
Rationale: Lewis, Goodman, Miller.

17. A multiple recursive generator (MRG) uses:
A. A linear combination of several previous values mod m
B. Only the previous value
C. Bit shifting only
D. No recursion
Correct Answer: A. A linear combination of several previous values mod m
Rationale: Higher-order recursion.

18. Poisson random variates can be generated by:
A. Box-Muller
B. Taking the maximum of uniforms
C. Inverse transform of a normal
D. Counting exponential interarrivals until their sum exceeds 1 (rate lambda), or multiplying uniforms
until the product drops below e^(-lambda)
Correct Answer: D. Counting exponential interarrivals until their sum exceeds 1 (rate lambda),
or multiplying uniforms until the product drops below e^(-lambda)
Rationale: Poisson process logic.