ABSTRACT
This chapter introduces two fundamental concepts of convergence for a sequence of random variables https://www.w3.org/1998/Math/MathML"> U n ; n ≥ 1 . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq3722.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> In Section 5.2, we discuss convergence in probability (denoted by https://www.w3.org/1998/Math/MathML"> → P https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq3723.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ) and the weak laws of large numbers (WLLN). Section 5.3 introduces the notion of convergence in distribution or law (denoted by https://www.w3.org/1998/Math/MathML"> → £ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq3724.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ). Slutsky’s Theorem sets some ground rules for manipulations involving both modes of convergence. Section 5.3 also includes the central limit theorem (CLT) for both sample mean (Theorem 5.3.3) and sample variance (Theorem 5.3.5). Some large-sample properties of Chisquare, https://www.w3.org/1998/Math/MathML"> t https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq3725.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , and https://www.w3.org/1998/Math/MathML"> F https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq3726.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> distributions are included in section 5.4.
