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| If $latex Z_1, \dots, Z_n$ are independent $latex \text{Cauchy}(0, 1)$ variables and $latex w= (w_1, \dots, w_n)$ is a random vector independent of the $latex Z_i$'s with $latex w_i \geq 0$ for all $latex i$ and $latex w_1 + \dots w_n = 0$, it is well-known that $latex \displaystyle\sum_{i=1}^n w_i Z_i$ also has a $latex...