# We can refer to be the accuracy level and to be the

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: real number. We say that the sequence Yn converges to a in probability, if for every ε &gt; 0, lim P (|Yn − a| ≥ ε ) = 0. n→∞ That is, for every ε &gt; 0, and for every δ &gt; 0, there exists some n0 so that P (|Yn − a| ≥ ε ) ≤ δ , ∀n ≥ n0 . We can refer ε to be the accuracy level, and δ to be the conﬁdent level. Intuition: for any given levels of accuracy and conﬁdence, for large enough n, Yn equals a within these levels of accuracy and conﬁdence. M. Chen (IE@CUHK) ENGG2430C lecture 10 14 / 29 The Weak Law of Large Number (LLN) Let X1 , X2 , . . . be a inﬁnity sequence of independent identically distributed r.v.s with mean µ . Deﬁne the sample mean (r.v.) sequence as Yn = X1 + X2 + · · · + Xn , n = 1, 2, . . . . n We have Yn converges to µ in probability as n → ∞, i.e., for any ε &gt; 0, lim P (|Yn − µ | ≥ ε ) = 0. n→∞ The only assumption: X1 , X2 , . . . are independent identically distributed Xi can follow any distribution, with ﬁnite mean (variance can be...
View Full Document

## This document was uploaded on 03/31/2014.

Ask a homework question - tutors are online