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Consider a random sample of size n from a gamma distribution, X, GAM(0, K), and let X = (1/n) [X, and X = (X)/ be the sample mean and geometric mean, respectively (a) Show that X and X are jointly complete and sufficient for 8 and K. (b) Find the UMVUE of μ = 0K. (c) Find the UMVUE of μ". (d) Show that the distribution of T = X/X does not depend on 0. (e) Show that X and T are stochastically independent random variables. () Show that the conditional pdf of X given X = x does not depend on K.

Consider a random sample of size n from a gamma distribution, X, GAM(0, K), and let X = (1/n) [X, and X = (X)/ be the sample mean and geometric mean, respectively (a) Show that X and X are jointly complete and sufficient for 8 and K. (b) Find the UMVUE of μ = 0K. (c) Find the UMVUE of μ". (d) Show that the distribution of T = X/X does not depend on 0. (e) Show that X and T are stochastically independent random variables. () Show that the conditional pdf of X given X = x does not depend on K.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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29. Consider a random sample of size n from a gamma distribution, X; - GAM(0, K), and let X = (1/n) X, and X = (I X)/n be the sample mean and geometric mean, respectively. (a) Show that X and X are jointly complete and sufficient for 0 and K. (b) Find the UMVUE of u = 0x. %3D (c) Find the UMVUE of µ". (d) Show that the distribution of T X/X does not depend on 0. (e) Show that X and T are stochastically independent random variables. (r) Show that the conditional pdf of X given X = i does not depend on K. %3D
Transcribed Image Text:29. Consider a random sample of size n from a gamma distribution, X; - GAM(0, K), and let X = (1/n) X, and X = (I X)/n be the sample mean and geometric mean, respectively. (a) Show that X and X are jointly complete and sufficient for 0 and K. (b) Find the UMVUE of u = 0x. %3D (c) Find the UMVUE of µ". (d) Show that the distribution of T X/X does not depend on 0. (e) Show that X and T are stochastically independent random variables. (r) Show that the conditional pdf of X given X = i does not depend on K. %3D
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