Let X 1 ,X 2 , . . .,X n be a random sample from the beta distribution with = = and

Let X₁,X₂, . . .,X_n be a random sample from the beta distribution with α = β = θ and Ω = {θ : θ = 1, 2}. Show that the likelihood ratio test statistic Λ for testing H₀ : θ = 1 versus H₁ : θ = 2 is a function of the statistic W = Σⁿ_i=1 log X_i + Σⁿ_i=1 log (1 − X_i).