Theorem A at Section 8.8.1 saysA necessary and sufficient condition for T(X1,..., Xn) to be sufficient for a parameter θ is that the joint probability function (density function or frequency function) factors in the formf(x1,...,xn|θ) = g[T(x1,...,xn),θ]h(x1,...,xn) 68. Let Xi, . . . , Xn be an 1.1.d. sample from a Poisson distribution with mean λ, anda. Show that the distribution of Xi,, Xn given T is independent of λ, andconclude that T is sufficient for λ.b. Show that X is not sufficient.c. Use Theorem A of Section 8.8.1 to show that T is sufficient. Identify thefunctions g and h of that theorem.

a.Proof for distribution of X1, X2… Xn given T is independent of λ.Sufficient statistics:A statistic…

Answered: 68. Let Xi, . . . , Xn be an 1.1.d.…

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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Theorem A at Section 8.8.1 says
A necessary and sufficient condition for T(X1,..., Xn) to be sufficient for a parameter θ is that the joint probability function (density function or frequency function) factors in the form
f(x1,...,xn|θ) = g[T(x1,...,xn),θ]h(x1,...,xn)

68. Let Xi, . . . , Xn be an 1.1.d. sample from a Poisson distribution with mean λ, and
a. Show that the distribution of Xi,
, Xn given T is independent of λ, and
conclude that T is sufficient for λ.
b. Show that X is not sufficient.
c. Use Theorem A of Section 8.8.1 to show that T is sufficient. Identify the
functions g and h of that theorem.

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