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Let the random variable X follow a uniform distribution in the interval [0,0]. Then the density function of X is if 0

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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Question

Let the random variable X follow a uniform distribution in the interval [0,0]. Then the
density function of X is
if 0<x<0
0, otherwise.
Consider a random sample of size n from this population.
(a) From the likelihood function of , argue that its maximum likelihood estimator is
the nth order statistic (Y₂).
f(x; 0) =
(b) Is the estimator in part (a) unbiased? If not, find an unbiased estimator of and
denote it by ₁. [Hint: Derive the distribution of Y₁-]

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Follow-up Questions

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Follow-up Question

(e) Show that ₂ = 2X, with X = 1 EX₁, is unbiased for 0.
(d) Obtain the relative efficiency of 2 with respect to ₁.

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Follow-up Question

(e) Show that ₂ = 2X, with X = 1X₁, is unbiased for 0.
(d) Obtain the relative efficiency of 2 with respect to ₁.

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