III. REVIEW QUESTIONS AND HOME WORK PROBLEMS
1. REVIEW QUESTIONS TO TEST UNDERSTANDING OF ORDINAL OPTIMIZATION
- In general it is easier to determine A > B (or A <
B) than to determine A - B = ?. (True or False)
- Under i.i.d. sampling, the confidence interval of the sample mean as
an estimate of the true mean decreases as
i. 1/n, where n is the number of samples taken
ii. 1/n1/2
iii. 1/n2
iv. a - bn, where a and b are constants
depending on the problem
- Suppose you randomly take 1,000 samples from an arbitrary distribution
and ordered these samples. The probability that at least one of the
observed samples belong in the top 1% of the underlying distribution
is
i. absolutely zero
ii. 1 - [(1 - 0.01)1000]
iii. (1 - 0.01)1000
iv. involving summing over a series with many terms too complicated
to write down here.
- In terms of ordinal optimization in the above problem assuming we are
maximizing, what is the "good enough" set, G, and what is
the 'selected' set, S?
i. G = top 1% of the distribution and S = the 1,000
samples
ii. G = the 1,000 samples and S = top 1% of the
distribution
iii. G = the largest value of the 1,000 samples and S =
the largest value of the distribution
iv. G= top 1% of the distribution and S = top 1% of the
1,000 samples
- The probability we are calculating in problem 3 is called the
"alignment probability" in ordinal optimization. (True or
False)
- The alignment probability approaches one exponenetially fast as we
increase the size of G and S. (True or
False)
- In OO, the existence of a non zero mean in the noise/error of the
Thurston model does not effect the alignment probability. (True or
False)