Question

Likelihood Ratio Tests - I only require (c) and (d) here.

I have posted (a) and (b) in another question

Let X1,..., Xn be a random sample from the distribution with pdf { 0-1e--)e f(r μ, θ ) - 0. where E Rand 0 > 0 (a) If 0 is known but a is unknown, find a likelihood ratio test (LRT) of size a for testing Η : μ> Ho Ho Ho versus where oi a known constant (b) If 0 is known but u is unknown, find a most powerful test (MPT) of size a for testing Η : μ= μι, H0 : μ= lο versus where o and are fixed real numbers satisfy 0< 4o< 41 (c) If both u and 0 are unknown, find a likelihood ratio test (LRT) of size a for testing H 00, Ho: 0 = 00 versus where >0 is a fixed real number. (Use quantiles of chi-square distributions to (X- X))~ Gamma(n - express the test) Hint: you may use the fact that 1,0) (d) Find a 1 a confidence set for 0 by inverting the test found in (c)

Answer 1

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