# Let X1, … , Xn be non-negative independent random variables with continuous distributions (but X1, … , XN are not necessarily identically distributed)…

**Question:**

Let X1, … , Xn be non-negative independent random variables with continuous distributions (but X1, … , XN are not necessarily identically distributed). Assume that the PDFs of Xi’s are uniformly bounded by 1. (a) Show that for every i, Eſexp(-tX;)] = Į, for all t > 0. (b) By using (a), show that for any e > 0, we have

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