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When transforming 2+ continuous random variables, you use a Jacobian matrix and compute the determinant. Do you also compute the Jacobian for discrete random variables?

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  • $\begingroup$ No. For example, consider a Poisson distribution on $x$ and $y$; if you transform the variables to $z_1=x^2$ and $z_2=y^2$, the probability of $(z_1,z_2)=(4,4)$ = the probability of $(x,y) = (2,2)$. $\endgroup$ – jbowman Apr 10 at 19:37
  • $\begingroup$ I don't see why you couldn't compute the Jacobian--but it would be irrelevant to any conceivable calculations you would want to do. What kind of calculation do you have in mind? $\endgroup$ – whuber Apr 10 at 20:21

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