If there are 3 i.i.d variables (X1, X2, and X3) with the same marginal probability density functions, but only 2 equations (Y1 and Y2) that contain some combination of those 3 variables, would it be possible to prove that those equations are independent of one another by developing a joint pdf f(Y1, Y2) and then proving that f(Y1, Y2) = f(Y1)*f(Y2), or would we need to use another method? I don't know how I would be able to develop a Jacobian with these equations.
2026-04-06 21:10:02.1775509802
Proving Independence with 3 different variables, but only 2 different equations
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