Homework 9 – STAT 543
Due Friday, March 30 by 5:00 pm (TA’s office);;
you also may turn in the assignment in class on the same Friday
Distance students: Due Friday, April 6 by 5:00 pm (TA’s email)
1. Consider one observation X from the probability density function
µ
¶
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2
f (x|θ) = 1 − θ x −
, 0 ≤ x ≤ 1,
−1 ≤ θ ≤ 1.
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Suppose we wish to test H0 : θ = 0 vs. H1 : θ 6= 0.
(a) For the above hypotheses, find the likelihood ratio test statistic λ(X) based on X (i.e., as a
function of X)
(b) For a given α ∈ (0, 1), find the size α likelihood ratio test (LRT) of the above hypotheses.
(Hint: Consider α < 1/2 or ≥ 1/2.)
2. Problem 8.5, Casella and Berger (2nd Edition)
3. Problem 8.6, Casella and Berger (2nd Edition)
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