Let \( \mathbf{x} = (x_1, \ldots, x_n) \) be a data set, and denote its sample standard deviation with \( s_x \). Let \( y_i = ax_i + b \).(a) Show that \( s_y = |a| s_x \), where \( s_y \) is the sample standard deviation of \( \mathbf{y} = (y_1, \ldots, y_n) \).(b) Show that \( Median(y) = a \cdot Median(x) + b \).(c) If \( a > 0 \), can you write the relation between \( Q1(y) \) and \( Q1(x) \)? What happens if \( a < 0 \)?**Note:** \( Q1(x) \) (or \( Q1(y) \)) denotes the first quartile of the distribution of the random variable \( x \) (or \( y \)).

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Answered: Let x = (x₁,...,xn) be a data set, and…

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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