For the hypothesis testing problem of Chapter 8, assume that there is a cost C 0 of choosing H=1 when H=0 is correct, and a cost C 1 of choosing H=0 when H=1 is correct. Show that a threshold test...

For the hypothesis testing problem of Chapter 8, assume that there is a cost C₀
of choosing H=1 when H=0 is correct, and a cost C₁
of choosing H=0 when H=1 is correct. Show that a threshold test minimizes the expected cost using the threshold η = (C₁p₁)/(C₀p₀).