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Theorem 2.2.6 (Hoeffding's inequality for general bounded random variables). Let X₁, XN be independent random variables. Assume that X₁ [m,, M.] for every i. Then, for any t > 0, we have N {(x₁ - EX;) ≥ 1} { i=1 21² Σ(Μ; – m;)2/ Prove Theorem 2.2.6, possibly with some absolute con- Exercise 2.2.7. stant instead of 2 in the tail. Sexp

Theorem 2.2.6 (Hoeffding's inequality for general bounded random variables). Let X₁, XN be independent random variables. Assume that X₁ [m,, M.] for every i. Then, for any t > 0, we have N {(x₁ - EX;) ≥ 1} { i=1 21² Σ(Μ; – m;)2/ Prove Theorem 2.2.6, possibly with some absolute con- Exercise 2.2.7. stant instead of 2 in the tail. Sexp

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Finish exercise 2.2.7

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Theorem 2.2.6 (Hoeffding's inequality for general bounded random variables). Let X1,..., XN be independent random variables. Assume that X; € [m;, M;] for every i. Then, for any t > 0, we have N 212 P (X; – E X;) > t} < exp E, (M, – m.)² i=1 Exercise 2.2.7. ** Prove Theorem 2.2.6, possibly with some absolute con- stant instead of 2 in the tail.
Transcribed Image Text:Theorem 2.2.6 (Hoeffding's inequality for general bounded random variables). Let X1,..., XN be independent random variables. Assume that X; € [m;, M;] for every i. Then, for any t > 0, we have N 212 P (X; – E X;) > t} < exp E, (M, – m.)² i=1 Exercise 2.2.7. ** Prove Theorem 2.2.6, possibly with some absolute con- stant instead of 2 in the tail.
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