Afind an lr test of size a for testing h01 2 versus h1 1

Question

Let X_i1, ..., X_ini , i = 1, 2, be two independent samples i.i.d. from the uniform distributions U(0, θ_i), i = 1, 2, respectively, where θ₁ > 0 and θ₂ > 0 are unknown.

(a) Find an LR test of size α for testing H₀;θ₁ =θ₂ versus H₁ ;θ₁ ≠ θ₂.

(b) Derive the limit distribution of -2 log λ, where λ is the likelihood ratio in part (a).