Some Product Moments Useful in Sampling Theory

Abstract

General methods are developed for finding the mathematical expectation of and where X pj denotes the p th ( p =1,2,···, k ) character of the j th ( j =1,2,···, N ) unit of a finite population, is the sample mean of the p th character based on a random sample of size n , and is the corresponding population mean. Methods for unbiasedly estimating the product moments are also presented.