Hypothesis Testing---II

• We are given our Standard N observations on which to make our decision.

• We do this by constructing yet another statistic Y which is some function of .

• We assume that Y has distribution if hypothesis i is true (i=0 or 1 if two hypotheses).

• Y could be vector valued but we will take scalar case here.

• In the best of all possible worlds, one can find a Y such that the values taken by it under two hypotheses are disjoint, i.e.,

  

• Unfortunately, Equation (36) is not always attainable

  but one should always try to minimize the probability overlap integral.