Let X1, . . . , Xn ∼ iid log Normal (µ, σ^2 ) for σ^...

Question

Question

Let X1, . . . , Xn ∼ iid log Normal (µ, σ^2 ) for σ^ 2 known. Find the LRT for H0 : µ = µ_0 vs H1 : µ not= µ_0.

f(x)=(2π)^(-1/2)(xσ)^(-1)*exp(-(ln x-µ)^2 /(2σ^2))

Answer 1

Answer #1

Let us write f0 and f1 as the density function under H0 and H1 respectively .By independence the joint density function of the sample under H0 is,

Where x^- = sample mean

Answer 2

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