Homework 9 – STAT 543
Due Friday, March 31 by 5:00 pm (TA’s office);
you also may turn in the assignment in class on the same Friday
1. Problem 8.5, Casella and Berger (2nd Edition)
2. Problem 8.17, Casella and Berger (2nd Edition)
3. Suppose that X has pdf f (x) = 2θ(1 − 2x) + 2x for x ∈ [0, 1], θ ∈ [0, 1]. Find the Bayes test for
H0 : θ ≤ 0.4 vs H1 : θ > 0.4 with respect to the uniform prior on [0, 1].
4. Suppose that X is a Poisson(λ) random variable and a Bayesian uses a prior for λ that is Exponential
with mean 1. Find the Bayes test for H0 : λ ≤ 2 vs H1 : λ > 2 and state the decision rule
(reject/don’t reject) for this test in terms of “X < c” vs “X ≥ c” for some c.
1