Let Y₁, Y₂, ..., Y₁ denote a random sample with density function given by Ae-Ay, 0 0. f(y|x) = a. Show that X = ₁₁Y₁ is sufficient for X. b. Use the mgf method to show that X~ Gamma(a = n, ß =). c. Show that is the MVUE for A.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Let Y₁, Y₂, ..., Y₁ denote a random sample with density function given by
Ae-Ay, 0<y<∞0,
0,
elsewhere,
where x > 0.
f(y|x) =
a. Show that X = ₁₁Y₁ is sufficient for X.
b. Use the mgf method to show that X~ Gamma(a = n, ß =).
c. Show that is the MVUE for A.
Transcribed Image Text:Let Y₁, Y₂, ..., Y₁ denote a random sample with density function given by Ae-Ay, 0<y<∞0, 0, elsewhere, where x > 0. f(y|x) = a. Show that X = ₁₁Y₁ is sufficient for X. b. Use the mgf method to show that X~ Gamma(a = n, ß =). c. Show that is the MVUE for A.
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