ABSTRACT
Let https://www.w3.org/1998/Math/MathML"> X 1 , … , X n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq2596.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> be https://www.w3.org/1998/Math/MathML"> n ( ≥ 2 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq2597.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> independent and identically distributed (iid) observations from a population. Now, we introduce some methods to find the probability distribution of a function of https://www.w3.org/1998/Math/MathML"> X 1 , … , X n . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq2598.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> For example, we handle a sample sum, https://www.w3.org/1998/Math/MathML"> ∑ i = 1 n X i https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq2599.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , a sample mean, https://www.w3.org/1998/Math/MathML"> X ‾ = n - 1 ∑ i = 1 n X i https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq2600.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , or a sample variance, https://www.w3.org/1998/Math/MathML"> S 2 = ( n - 1 ) - 1 ∑ i = 1 n X i - X ‾ 2 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq2601.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . We also explore the distributions of https://www.w3.org/1998/Math/MathML"> X 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/eq2602.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , the smallest observation, and https://www.w3.org/1998/Math/MathML"> X n : n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429113741/fa82963e-6109-44c7-ad13-faec498214f4/content/eq2603.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , the largest observation. These probability distributions are called sampling distributions.
