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)
   
   Ans: T
   
   
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/n^1/2
   iii. 1/n²
   iv. a - bn, where a and b are constants depending on the problem
   
   Ans: ii
   
   
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.
   
   Ans: ii
   
   
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
   
   Ans: i
   
   
5. The probability we are calculating in problem 3 is called the "alignment probability" in ordinal optimization. (True or False)
   
   Ans: T
   
   
6. The alignment probability approaches one exponenetially fast as we increase the size of G and S. (True or False)
   
   Ans: T
   
   
   
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)
   
   Ans: T