Question

1. Consider two probability density functions on [0, 1], f0(x) = 2x and f1(x) = 2/(x + 1)2 . •

(a) Construct the most powerful test for H0 : X ∼ f0 against HA : X ∼ f1 with the significance level α = 0.05. •

(b) Find its power. •

(c) Suppose we observe X = 1/3. What is the p-value of the test in 1(a).

Answer 1