Let (Xr; r ? 1) be independent random variables, such th
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Let (Xr; r ? 1) be independent random variables, such that Xr is Exponential (?r), where 0 < ? r=1 ?r < ?. Let Y = infr?
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Let (Xr; r ? 1) be independent random variables, such that Xr is Exponential (?r), where 0 < ? r=1 ?r < ?. Let Y = infr?1 Xr. Show that with probability 1 there is a unique N such that XN = Y, and P(N = r) = ?r ? r=1 ?r. Prove that Y and N are independent.
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