Let X1,..., XN be i.i.d. random variables with a uniform distribution of (0, 0]. Consider the following estimator: = max (X1,...,XN) (a) Show that the PDF of ê is fa(@) = N (Fx (x)}^=1 fx(x), where fx and Fx are the PDF and CDF of Xn (b) Show that ê is a biased estimator. (c) Find a constant c so that ce is unbiased.

Let X1,..., XN be i.i.d. random variables with a uniform distribution of (0, 0]. Consider the following estimator: = max (X1,...,XN) (a) Show that the PDF of ê is fa(@) = N (Fx (x)}^=1 fx(x), where fx and Fx are the PDF and CDF of Xn (b) Show that ê is a biased estimator. (c) Find a constant c so that ce is unbiased.

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 i.i.d. random variables with a uniform distribution of [0, 0]. Consider the
following estimator:
6(X) = max (X1,..., XN)
%3D
(a) Show that the PDF of O is fa (0) = N [Fx(r)]N-fx(x), where fx and Fx are the PDF
and CDF of Xn
(b) Show that ê is a biased estimator.
(c) Find a constant c so that cO is unbiased.
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