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Consider the experiment of rolling two tetrahedra that are unfair in the sense that each has the following probabilities for each of the four faces:
Let X be the total of the outcomes in the two tetrahedra and Y be the absolute difference between their outcomes. Obtain the joint probability mass function of (X,Y).
So I am confused on how to do the probabilities since it is a biased experiment. My professor taught us how to do it for two fair tetrahedra but when I do the same method except with the biased probabilities I can't seem to get anything right. How exactly do you do this?
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Since there are only eight possible outcomes, why not list them all with their probabilities?
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