MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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 f(x;0) S, 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 (Y). (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.] (c) Show that ₂ = 2X, with X = X₁, is unbiased for 0.
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Transcribed Image Text:Let the random variable X follow a uniform distribution in the interval [0,0]. Then the density function of X is f(x;0) S, 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 (Y). (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.] (c) Show that ₂ = 2X, with X = X₁, is unbiased for 0.
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