1. Math
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  3. 2 suppose that we have n independent observations x1 xn...

Question: 2 suppose that we have n independent observations x1 xn...

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2. Suppose that we have n independent observations x1,..., xn from a normal distribution with mean μ and variance σ, and we want to test (a) Find the maximum likelihood estimator of μ when the null hypothesis is true. (b) Calculate the Likelihood Ratio Test Statistic 2 lo g max L(μ, σ log | max L( 1) (c) Explain as clearly as you can what happens to T when our estimate of σ2 is less than 1. (d) Show that the LRT test is the same as a test which rejects the null hypothesis when s2 > c

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