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Consider the following probability density function of the random variable X: fx (2:0) = -√e-12-01 fx(x; -|x-0| with R. If we sample an odd number n (i.e. n = 2m+1) of i.i.d. RVs X₁,..., Xn, show that the MLE of is the median of the sample (the observation such that half of the rest of the observations are smaller and half larger).

Consider the following probability density function of the random variable X: fx (2:0) = -√e-12-01 fx(x; -|x-0| with R. If we sample an odd number n (i.e. n = 2m+1) of i.i.d. RVs X₁,..., Xn, show that the MLE of is the median of the sample (the observation such that half of the rest of the observations are smaller and half larger).

MATLAB: An Introduction with Applications
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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: Consider the following probability density function of the random variable X: 1 fx (x; 0) = ₂-|x-01 = 2 with x € R. If we sample an odd number n (i.e. n = 2m +1) of i.i.d. RVs X₁,..., Xn, show that the MLE of is the median of the sample (the observation such that half of the rest of the observations are smaller and half larger).
Transcribed Image Text:: Consider the following probability density function of the random variable X: 1 fx (x; 0) = ₂-|x-01 = 2 with x € R. If we sample an odd number n (i.e. n = 2m +1) of i.i.d. RVs X₁,..., Xn, show that the MLE of is the median of the sample (the observation such that half of the rest of the observations are smaller and half larger).
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