Consider two random vectors $X\equiv (X_1,..., X_M)$ and $V\equiv (V_1,..., V_N)$. Suppose that $X\perp V$, where $\perp$ denotes stochastic independence.
Does this imply $W\equiv (X_1-X_M, X_2-X_M,..., X_{M-1}-X_{M})\perp V$?
2026-03-26 03:18:36.1774495116
Stochastic independence is preserved for linear combinations?
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