Sample Statistics and their Distributions
Vijay Kumar Rohatgi, A. K. Md. Ehsanes Saleh · Wiley series in probability and statistics · 2015
This chapter focuses on some problems of mathematical statistics. It first introduces the notions of (simple) random sample and sample statistics and focuses on sample moments and their exact distributions. The chapter then considers some important distributions that arise in sampling from a normal population, namely, chi-square , t-, and F-distributions. The final section of the chapter is devoted to the study of sampling from univariate and bivariate normal distributions. Various moments of noncentral t-distribution may be computed by using the fact that expectation of a product of independent random variables is the product of their expectations.