If {X1 X2, X3,..., Xk} is independent, show that {X1, X1 + X2, X1, + X2 +

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If {X1 X2, X3,..., Xk} is independent, show that {X1, X1 + X2, X1, + X2 + X3,..., X1 + X2 + ∙ ∙ ∙ + Xk} is also independent.
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