Problem 1 (Techniques of Chernoff Bound) (12+12-24 points) Let X1, Xy be non-negative independent random variables with
Posted: Fri Dec 24, 2021 10:01 am
- Problem 1 Techniques Of Chernoff Bound 12 12 24 Points Let X1 Xy Be Non Negative Independent Random Variables With 1 (23.75 KiB) Viewed 76 times
Problem 1 (Techniques of Chernoff Bound) (12+12-24 points) Let X1, Xy 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(-+X:)]<, for all t > 0. (b) By using (a), show that for any e > 0, we have N P P(X SEN) S (es) ial (Hint: For any t > 0, PEN X: SEN) = Ple'EXX SeteN)=P(e-1.X > e-teN))