ISYE 6644 ISYE 6644 Midterm

ISYE 6644 / ISYE 6644 Midterm Exam 2 ( Update 2025 / 2026) Simulation and Modeling for Engineering and Science Module 5,

• & 7 Questions & Answers Grade

A - Georgia Tech

Question:

Choosing a Good Generator Geometric Considerations

Answer:

Theorem: The k-tuples (Ri, ..., Ri+k1) i>=1,

from multiplicative generators lie on parallel hyperplanes in [0,1]^k.

Question:

Minimum number of hyperplanes (in all directions).

Answer:

Find the multiplier that maximizes this number. 1 / 4

Question:

Maximum distance between parallel hyperplanes

Answer:

Find the multiplier that minimizes this number

Question:

Minimum Euclidean distance between adjacent k-tuples

Answer:

Find the multiplier that maximizes this number.

Question:

Remark: The RANDU generator is particularly bad

Answer:

since it lies on only 15 hyperplanes.

• / 4

Question:

Serial Correlation of LCGs

Answer:

Question:

Goodness-of-fit tests

Answer:

are the PRNs approximately Unif(0,1)?

Question:

Independence tests

Answer:

are the PRNs approximately independent?

• / 4

Question:

If a particular generator passes both types of tests (in addition to other tests that we won't tell you about

Answer:

we'll be happy to use the PRNs it generates.

Question:

We regard as the status quo,

Answer:

so we'll only reject H0 if we have "ample" evidence against it. (Innocent until proven guilty.)

• / 4