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Let XaZ + b where Z~ N(0, 1) and a and b are real numbers with a > 0. Find the density function of X and hence show that X~ N(μ=b, o² = a²).

Let XaZ + b where Z~ N(0, 1) and a and b are real numbers with a > 0. Find the density function of X and hence show that X~ N(μ=b, o² = a²).

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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Let \( X = aZ + b \) where \( Z \sim N(0,1) \) and \( a \) and \( b \) are real numbers with \( a > 0 \). Find the density function of \( X \) and hence show that \( X \sim N(\mu = b, \sigma^2 = a^2) \).
Transcribed Image Text:Let \( X = aZ + b \) where \( Z \sim N(0,1) \) and \( a \) and \( b \) are real numbers with \( a > 0 \). Find the density function of \( X \) and hence show that \( X \sim N(\mu = b, \sigma^2 = a^2) \).
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