A decision making problem

silicon2006@hotmail.com · science forum beginner Joined: 19 May 2006 Posts: 6

''A' and 'B' are two sets.

'A'={x1, x2, x3}, where x1, x2 and x3 are Gaussian random variables
with the same standard deviation s but different mean a1, a2, a3. It
is known that a1>a2>a3. The specific magnitude of s is unknown.

Similarly, 'B'={y1, y2, y3}, with corresponding mean b1>b2>b3. The
standard deviation 's' is the same as in set 'A'.

It is known that a1>b1, a2>b2 and a3>b3.

Now, we have two sets of measurements from 'A' and 'B'. The results
are:
P={p1>p2>p3}, Q={q1>q2>q3}. We try to figure out which measurement is
from 'A' and which is from 'B'.

Remember that p1, p2, p3 and x1, x2, x3 (or y1, y2, y3) may not in the
same order. For example, p1 might be the random variable with mean b3
in set 'B'.

A simple way to tell whether measurement 'P' or 'Q' is from set 'A' is
to compare the average
pp=(p1+p2+p3)/3, qq=(q1+q2+a3)/3 and see which one is larger. Is it the
best judgement? or there is another approach which best utilizes the
information?

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