Let X be a random variable with PDF fx. Find the PDF of the random variable Y where Y= 3X for X> 0, and Y = -X/4 for X < 0, (sketch this relation in the x-y plane) a) Find the pdf and mean of Y in terms of fx. b) Do a) if X has a uniform pdf between –1 and 2. c) Do a) if X has a exponential pdf with 2=2.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Let X be a random variable with PDF fx. Find the PDF of the random variable Y
where Y= 3X for X> 0, and Y = -X/4 for X < 0, (sketch this relation in the x-y plane)
a) Find the pdf and mean of Y in terms of fx.
b) Do a) if X has a uniform pdf between -1 and 2.
c) Do a) if X has a exponential pdf with 2=2.
Transcribed Image Text:Let X be a random variable with PDF fx. Find the PDF of the random variable Y where Y= 3X for X> 0, and Y = -X/4 for X < 0, (sketch this relation in the x-y plane) a) Find the pdf and mean of Y in terms of fx. b) Do a) if X has a uniform pdf between -1 and 2. c) Do a) if X has a exponential pdf with 2=2.
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