Let X1,,X, be iid with Ba (e (z 0) >0, Sx(x) = otherwise. Here 6 is an unkown population parameter. Show that X- 0 has an Exponcntial(1) distribution. Find the method of moment estimator for 0. Let's call this 6 Is ôj unbiased for 0 ? Explain with precise computation.

Let X1,,X, be iid with Ba (e (z 0) >0, Sx(x) = otherwise. Here 6 is an unkown population parameter. Show that X- 0 has an Exponcntial(1) distribution. Find the method of moment estimator for 0. Let's call this 6 Is ôj unbiased for 0 ? Explain with precise computation.

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let X1, , Xn be iid with population density
Je (z
Sx(x) =
r > 0,
otherwise.
Here 0 is an unkown population parameter.
Show that X-0 has an Exponential(1) distribution.
Find the method of moment estimator for 0. Let's call this 6.
Is ôj unbiased for 0 ? Explain with precise computation.
Find the maximum likelihood estimator for 6. Let's call this Ô2.
Is ô, unbiased for 0 ? Explain with precise conputation.

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