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You are given the probability distribution function (PDF) of a continuous random variable X is fy(x). Let Y be a continuous random variable such that Y = aX + b, where a and b are non-zero real constants. 1. Find the PDF of Y in terms of fx, a, and 5. 2. Let X be an exponential random variable with parameter 1. When will Y also be an exponential random variable? 3. Let X be a normal random variable with mean u and variance o² . When will Y also be a normal random variable?

You are given the probability distribution function (PDF) of a continuous random variable X is fy(x). Let Y be a continuous random variable such that Y = aX + b, where a and b are non-zero real constants. 1. Find the PDF of Y in terms of fx, a, and 5. 2. Let X be an exponential random variable with parameter 1. When will Y also be an exponential random variable? 3. Let X be a normal random variable with mean u and variance o² . When will Y also be a normal 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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Note: Subparts 2 and 3 must be answered using only the formula derived in subpart 1. You can use Method of Transforms in subpart 1 however it is not necessary to use it.
Transcribed Image Text:Note: Subparts 2 and 3 must be answered using only the formula derived in subpart 1. You can use Method of Transforms in subpart 1 however it is not necessary to use it.
You are given the probability distribution function (PDF) of a continuous random variable X is fx(x). Let Y be a continuous random variable such that Y = aX + %3D b, where a and b are non-zero real constants. 1. Find the PDF of Y in terms of fx, a, and b. 2. Let X be an exponential random variable with parameter 2. When will Y also be an exponential random variable? 3. Let X be a normal random variable with mean u and variance o² . When will Y also be a normal random variable?
Transcribed Image Text:You are given the probability distribution function (PDF) of a continuous random variable X is fx(x). Let Y be a continuous random variable such that Y = aX + %3D b, where a and b are non-zero real constants. 1. Find the PDF of Y in terms of fx, a, and b. 2. Let X be an exponential random variable with parameter 2. When will Y also be an exponential random variable? 3. Let X be a normal random variable with mean u and variance o² . When will Y also be a normal random variable?
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