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Question 5 Suppose X is a normal random variable with mean μ and variance o². (i) If a and b are constants, show that aX+b has a normal distribution and find its mean and variance. (ii) If Z = (X-μ)/o, deduce that Z N (0, 1). (iii) Using (ii) find P(X < x) in terms of I, where is the cumulative distribution function of a N(0, 1) random variable.

Question 5 Suppose X is a normal random variable with mean μ and variance o². (i) If a and b are constants, show that aX+b has a normal distribution and find its mean and variance. (ii) If Z = (X-μ)/o, deduce that Z N (0, 1). (iii) Using (ii) find P(X < x) in terms of I, where is the cumulative distribution function of a N(0, 1) random variable.

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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Question 5 Suppose X is a normal random variable with mean and variance o². (i) If a and b are constants, show that aX + b has a normal distribution and find its mean and variance. (ii) If Z = (X − μ)/o, deduce that Z~ N(0, 1). (iii) Using (ii) find P(X < x) in terms of Þ, where is the cumulative distribution function of a N(0, 1) random variable. (iv) If c> 0 is a constant, show that P(µ – co < X < μ+co) does not depend on μ or o.
Transcribed Image Text:Question 5 Suppose X is a normal random variable with mean and variance o². (i) If a and b are constants, show that aX + b has a normal distribution and find its mean and variance. (ii) If Z = (X − μ)/o, deduce that Z~ N(0, 1). (iii) Using (ii) find P(X < x) in terms of Þ, where is the cumulative distribution function of a N(0, 1) random variable. (iv) If c> 0 is a constant, show that P(µ – co < X < μ+co) does not depend on μ or o.
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