CHAPTER 10 - SUM OF A RANDOM NUMBER OF INDEPENDENT RANDOM VARIABLES

Abstract

This chapter focuses on the sum of a random number of independent random variables. A law of large numbers states that the average of the first n terms of a sequence of random variables is practically constant if n is large enough. In many practical applications, the number of the experiments depends on chance. The chapter describes the conditions on {vn} under which ζn 0 implies ζn ⇒ 0. The usual restriction is that vn/n tends to a positive constant in probability. This condition implies that a <vn <b with probability close to 1.