I have $6$ random variables $a,b,c,d,f,g$, each having independent Gaussian distribution. Now I define following three random variables \begin{equation} X = ab - cd\\ Y = cf - ag\\ Z = gd - bf \end{equation} where, $X^2+Y^2+Z^2=\text{constant}$. The value of the constant is not known to me. Can I say that the distributions of $X,Y,Z$ are independent of each other?
2026-05-15 15:05:52.1778857552
Are functions of independent random variables related to each other by a constant independent
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