√2π elsewhere i) Show that f(x; 0) belongs to the one-parameter regular exponential family. Clearly indicate the following functions, h(x), c(0), w(0) and t(x). ii) Show that = X is the maximum likelihood estimator of the parameter 8. iii) Is the maximum likelihood estimator = 1X₁, an efficient estimator of 8?
√2π elsewhere i) Show that f(x; 0) belongs to the one-parameter regular exponential family. Clearly indicate the following functions, h(x), c(0), w(0) and t(x). ii) Show that = X is the maximum likelihood estimator of the parameter 8. iii) Is the maximum likelihood estimator = 1X₁, an efficient estimator of 8?
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:b) Suppose that a sequence of mutually independent and identically distributed continuous
random variables X₁, X₂, X3X₁ has the probability density function
1
(x-8)²
2 for -00<x<∞⁰
f(x: 0)=√√2
0
elsewhere
i) Show that f(x; 8) belongs to the one-parameter regular exponential family. Clearly
indicate the following functions, h(x), c(0), w(8) and t(x).
ii) Show that = -1 X is the maximum likelihood estimator of the parameter 8.
iii) Is the maximum likelihood estimator
iv) If 0₁ = X₁ - 2X₂ + 2X₁ and ₂ = X₁
relative efficiency of ₂ with respect to 8₁?
===1X₁, an efficient estimator of ?
X₂ + X, are unbiased estimators of 8. What is the
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