MGF of the Affine Transformation of two uniform random variables.

garthenar

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Apr 23, 2021
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Transcription of Problem
Y is a uniform distribution between (α, β)
X is a uniform distribution between (0,1)
The affine transformation is
y = (β-α)x + α <------- I don't get how he's getting this or how it relates to an affine transformation
After that I have to get the MGF (EDIT: Which I have done)

Background (what we're working on in class)
This class has been focused around probability theory (from what I understand) (E.G. PMF, PDF, CDF, now MGFs)
We are currently working on MGFs (Moment Generating Functions)
The previous example involved getting the MGF of a uniformly distributed random variable which I did.

Work So Far
I've researched what an affine transform is and related topics and learned a lot, but nothing about equations or how it applies to random variables. I stopped when things started going into group theory as we have only ever mentioned set theory. (Side note, I'm an engineer and things got pretty heavy into math theory)

Thread Choice
I'm assuming this belongs in the Advanced Math section because I've completed courses through Differential Equations and Linear Algebra and this wasn't mentioned.
 
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