Let the components of the vector x = [x1, xd]T he binary-valued (0 or 1), with d odd, and
pit=P(xi=11w1)=p>1/2 i= Pi2 = P(xi = 11w2) = 1 P i=
and P(w1) = P(w2) = 1/2. Suppose that xi’s are independent. Show that the minimum-error-rate decision rule becomes
Decide col if E xi > d/2 and (4)2 otherwise.
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