2. A sample of five observations is taken on a b(1,) RV to test H0 : ...

2. A sample of five observations is taken on a b(1,θ) RV to test H0 : θ = 12 against H1 : θ = 34

.

(a) Find the most powerful test of size α = 0.05.

(b) If L( 1 2 , 12

) = L( 3 4 , 34

) = 0, L( 1 2 , 34

) = 1, and L( 3 4 , 12

) = 2, find the minimax rule.

(c) If the prior probabilities of θ = 12 and θ = 34 are π0 = 13 and π1 = 23

, respectively, find the Bayes rule.