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Prove the following Theorem: Let X₁,..., X, be iid observations from a pdf or pmf f(z) that belongs to an exponential family given by S({z}8) — A(z)c(@?exp (Ém(1)t,(a)). f(x Σ TUX)-(XX)) where @ = (0,,04), d ≤ k. Then is a sufficient statistic for 6.

Prove the following Theorem: Let X₁,..., X, be iid observations from a pdf or pmf f(z) that belongs to an exponential family given by S({z}8) — A(z)c(@?exp (Ém(1)t,(a)). f(x Σ TUX)-(XX)) where @ = (0,,04), d ≤ k. Then is a sufficient statistic for 6.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 31E
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Prove the following Theorem: Let X₁,..., X₂, be iid observations from a pdf or pmf f(z) that belongs to an exponential family given by (Źw.(09)t.(z)), £4(X)) f(x)=h(x)c(@)expw)t(x where = (01,...,04), d≤k. Then T(x) = (24(x;), - j-1 is a sufficient statistic for.
Transcribed Image Text:Prove the following Theorem: Let X₁,..., X₂, be iid observations from a pdf or pmf f(z) that belongs to an exponential family given by (Źw.(09)t.(z)), £4(X)) f(x)=h(x)c(@)expw)t(x where = (01,...,04), d≤k. Then T(x) = (24(x;), - j-1 is a sufficient statistic for.
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