Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X; has proba- bility mass function P(Xį = x₁) = 2 (1–0)1-\zi, xi€{−1,0,1}, 0<0<1. a. Derive the MLE Ô for 0. b. Assuming n is large, find the approximate distribution of . c. Find an approximate 95% confidence interval for 0. d. Derive the likelihood ratio test for testing 0 = 1/2 vs. 0 > 1/2.
Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X; has proba- bility mass function P(Xį = x₁) = 2 (1–0)1-\zi, xi€{−1,0,1}, 0<0<1. a. Derive the MLE Ô for 0. b. Assuming n is large, find the approximate distribution of . c. Find an approximate 95% confidence interval for 0. d. Derive the likelihood ratio test for testing 0 = 1/2 vs. 0 > 1/2.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X, has proba-
bility mass function
P(X = x) = (9) (1 - 0)¹-|¹i|, x¡ € {−1,0,1}, 0≤0 ≤ 1.
2
a. Derive the MLE Ô for 0.
b. Assuming n is large, find the approximate distribution of .
c. Find an approximate 95% confidence interval for 0.
d. Derive the likelihood ratio test for testing = 1/2 vs. 0 > 1/2.
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