Statement of a problem № m41044


Consider a single observation X from a Cauchy distribution centered at θ. That is, the p.d.f. of X is Suppose that we wish to test the hypotheses H0: θ ≤ θ0, H1: θ >θ0. Let δc be the test that rejects H0 if X ≥ c. a. Show that π(θ|δc) is an increasing function of θ. b. Find c to make δc have size 0.05. c. If X = x is observed, find a formula for the p-value.

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