Let X₁, X2,..., Xn and Y₁, Y2,..., Yn be independent random samples from two normal distributions N(₁,02) and N(μ2,02), respectively, where o² is the common but unknown variance. Find the likelihood ratio A for testing Ho: 1 = 2 = 0 against all alterna- tives.

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Let X₁, X2,..., Xn and Y₁, Y2,..., Yn be independent random samples from
two normal distributions N(1,02) and N(μ2,02), respectively, where o² is the
common but unknown variance.
Find the likelihood ratio A for testing Ho: ₁ = 2 = 0 against all alterna-
tives.
Rewrite A so that it is a function of a statistic Z which has a well-known
distribution.
Transcribed Image Text:Let X₁, X2,..., Xn and Y₁, Y2,..., Yn be independent random samples from two normal distributions N(1,02) and N(μ2,02), respectively, where o² is the common but unknown variance. Find the likelihood ratio A for testing Ho: ₁ = 2 = 0 against all alterna- tives. Rewrite A so that it is a function of a statistic Z which has a well-known distribution.
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