Let V be as defined in Eq. (9.7.4). We wish to determine the size 0 likelihood ratio

Question:

Let V be as defined in Eq. (9.7.4). We wish to determine the size α0 likelihood ratio test of the hypotheses (9.7.7). Prove that the likelihood ratio test will reject H0 if either V ≤ c1 or V ≥ c2, where Pr(V ≤ c1) + Pr(V ≥ c2) = α0 when σ21 = σ22.