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 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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Transcribed Image Text: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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(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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Transcribed Image Text:(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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(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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Transcribed Image Text:(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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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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Transcribed Image Text:(e) Show that ₂ = 2X, with X = 1 EX₁, is unbiased for 0. (d) Obtain the relative efficiency of 2 with respect to ₁.
Solution
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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.
expand button
Transcribed Image Text:(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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