Abstract

This chapter discusses Riemann integration of real-valued functions, including a study of improper Riemann integrals, and convergence of a sequence of Riemann integrals. It also covers the Riemann–Stieltjes integral. Applications in statistics are given in the last section, which includes a discussion on the existence of the first negative moment of a continuous distribution, transformations of continuous random variables, and the Riemann–Stieltjes integral representation of the expected value of a random variable.

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