Joint pmf of 2 binomially distributed random variables

cimmerian
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I hope I wrote that correctly but I'm trying to find the joint. I heard it was impossible from someone.

X = A/R
A~BIN(n1, p1)
R~BIN(n2, p2)

I know I shouldn't be using the Jacobian method for Discrete distributions but I have to do it anyway.

Anyone know?
 
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The major difficulty arises from the fact that P(R=0) > 0, so you have a non-zero probability of X being infinite.
 

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