## III. REVIEW QUESTIONS AND HOME WORK PROBLEMS

#### 1. REVIEW QUESTIONS TO TEST UNDERSTANDING OF ORDINAL OPTIMIZATION

1. In general it is easier to determine A > B (or A < B) than to determine A - B = ?. (True or False)

2. 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

3. 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.

4. 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

5. The probability we are calculating in problem 3 is called the "alignment probability" in ordinal optimization. (True or False)

6. The alignment probability approaches one exponenetially fast as we increase the size of G and S. (True or False)

7. 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)