Let (X 1 , Y 1 ),(X 2 , Y 2 ),...,(X n , Y n ) be a random sample from a bivariate normal distribution with μ 1 , μ 2 , σ 2 1 = σ 2 2 = σ 2 , ρ =   , where μ 1 , μ 2 , and σ 2 > 0 are unknown real...

Let (X₁, Y₁),(X₂, Y₂),...,(X_n, Y_n) be a random sample from a bivariate normal distribution with μ₁, μ₂, σ²
₁
= σ²
₂
= σ², ρ =
  , where μ₁, μ₂, and σ²
> 0 are unknown real numbers. Find the likelihood ratio Λ for testing H₀
: μ₁
= μ₂
= 0, σ²
unknown against all alternatives. The likelihood ratio Λ is a function of what statistic that has a well-known distribution?