Suppose that X N ( 1 , 2 ), both unknown. We plan to test H 0 : 1 = 0,

 Suppose that X ∼ N (θ₁, θ₂), both unknown.  We plan to test H₀:  θ₁  = 0, θ₂  = 1 vs.  H₁: θ₁ = 1, θ₂ = 3. Find the simplest expression you can for a BCR in this setting. Assume a random sample of size n.