(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given a probability space, how do I find the family of all equivalent probabilities on the space?

For example,

let the discrete random variable X have uniform probability equal to 1/3, taking values 10, 2, and -3. the r.v. is represented on the finite probability space = {1, 2, 3}. How do I find the family of all equivalent probabilties?

2. Relevant equations

3. The attempt at a solution

my thought would be should I be using the Radon-Nikodym Theorem? (which I honestly am not so familiar with). Or is the solution far simpler than that.

All I ask is a direction or hint to work on first. thanks!

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# Equivalent probabilties

Can you offer guidance or do you also need help?

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