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(as a function of a) is minimized at any a = m, where m is th that is, a value such that Pr(X 2 m) 1/2 and Pr(X

(as a function of a) is minimized at any a = m, where m is th that is, a value such that Pr(X 2 m) 1/2 and Pr(X

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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(1) Let X be a random variable with EX| < 00. Show that the mean absolute error E|X – a| (as a function of a) is minimized at any a = m, where m is the median of X, that is, a value such that Pr(X > m) 2 1/2 and Pr(X < m) 2 1/2. (2) Conclude from (a) that for any given 1,..., I, €R, |I; – a| is minimized at the sample median, that is, at m = 1(n+1)/2) when n is odd and m = (1/2){r(m/2) + I(n/2+1)} when n is even.
Transcribed Image Text:(1) Let X be a random variable with EX| < 00. Show that the mean absolute error E|X – a| (as a function of a) is minimized at any a = m, where m is the median of X, that is, a value such that Pr(X > m) 2 1/2 and Pr(X < m) 2 1/2. (2) Conclude from (a) that for any given 1,..., I, €R, |I; – a| is minimized at the sample median, that is, at m = 1(n+1)/2) when n is odd and m = (1/2){r(m/2) + I(n/2+1)} when n is even.
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