Let X 1 , X 2 ..X n be a random sample from a distribution with pmfp(x; ) x = x (1 )

Let X ₁ , X ₂ …..X _n be a random sample from a distribution with pmfp(x; θ) ^x = θ ^x (1 – θ) ^1-x ,x= 0,1,

where 0 < θ < 1. We wish to test H ₀ : θ = 1/3versus H ₁ :6 1/3.
(a) Find Λ and -2Iog Λ.
(b) Determine the Wald-type test.
(c) What is Rao's score statistic?