Random Sums and Sequences
This chapter forms a bridge between the study of random variables in the previous chapters and the study of random processes to follow. A random process is simply a random function of time. If time is discrete, then such a random function could be viewed as a sequence of random variables. Even when time is continuous, we often choose to sample waveforms (whether they are deterministic or random) in order to work with discrete time sequences rather than continuous time waveforms. Thus, sequences of random variables will naturally occur in the study of random processes. In this chapter, we will develop some basic results regarding both finite and infinite sequences of random variables and random series.