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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 64E
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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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