Please no written by hand solutions please show all work for thumbs up and explain work within reason. just do parts b,c,d,e. the function is e^(2*theta) if you have trouble seeing it. 1. Let X_{1} ,...,X n denote a random sample from a Poisson distribution with parameter theta > 0 a. Is a Poisson family exponential? Justify your answer. b. Deduce from part a. that T= sum i = 1 to n X i i a complete sufficient statistic for theta c. Define h(X 1 ,...,X n )= (- 1) ^ X Show that h (X 1 ,...,X n ) is an unbiased estimator of r(theta) = e ^ (- 2theta) d. Show that the conditional probability mass function for X_{1} given T = t is Binomial ( mathfrak l , 1 n ) e. Find the UMVUE of r(theta) = e ^ (- 2theta).
Please no written by hand solutions please show all work for thumbs up and explain work within reason. just do parts b,c,d,e. the function is e^(2*theta) if you have trouble seeing it. 1. Let X_{1} ,...,X n denote a random sample from a Poisson distribution with parameter theta > 0 a. Is a Poisson family exponential? Justify your answer. b. Deduce from part a. that T= sum i = 1 to n X i i a complete sufficient statistic for theta c. Define h(X 1 ,...,X n )= (- 1) ^ X Show that h (X 1 ,...,X n ) is an unbiased estimator of r(theta) = e ^ (- 2theta) d. Show that the conditional probability mass function for X_{1} given T = t is Binomial ( mathfrak l , 1 n ) e. Find the UMVUE of r(theta) = e ^ (- 2theta).
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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Please no written by hand solutions
please show all work for thumbs up and explain work within reason. just do parts b,c,d,e. the
1. Let X_{1} ,...,X n denote a random sample from a Poisson distribution with parameter
theta > 0
a. Is a Poisson family exponential? Justify your answer.
b. Deduce from part a. that T= sum i = 1 to n X i i a complete sufficient statistic for theta
c. Define
h(X 1 ,...,X n )= (- 1) ^ X
Show that h (X 1 ,...,X n ) is an unbiased estimator of r(theta) = e ^ (- 2theta)
d. Show that the conditional probability mass function for X_{1} given T = t is Binomial ( mathfrak l , 1 n )
e. Find the UMVUE of r(theta) = e ^ (- 2theta).
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