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√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?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 3CR
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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
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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