III. HOME WORK PROBLEMS
6. GOAL SOFTENING (2)
Consider the same question as above, except now the population is finite
[i = 1, 2, ..., N] with Ji = i. But we
must observe Ji through N(0,1) additive noise,
Jobserved = Jactual + w
where w ~ N(0,1).
If it help to simplify things, you can choose a specific value for N,
say N = 3 or 5.
- What is the probability that if we choose the observed top value out
of the population it will turn out to be indeed the true top
- What is the probability that if we choose the 2 observed top values,
at least one of them will turn out to be among the actual top-2
- Can you generalize the above?