 Two Problems 1. Briefly describe the following: (a) how to connect 1000 users to one another without directly connecting every user to every other one. (b) two ways to put 1000 users on a single wire. (c) the cellular concept. 2. Describe three communication systems that send their signal as an EM wave through the atmosphere. 3. On your own, find on the web or in the library a telecommunication system not described in this chapter (e.g., HDTV, the Internet) and provide a two-page overview, highlighting how the system works. Chapter A Review of Some Important Math, Stats, and Systems y intention in writing this chapter is to give a quick review of key mathematical, statistical, and engineering concepts which we'll use in our study of telecommu- nications. I basically provide a brief review of random variables and random processes, and then talk in passing about the Fourier transform and linear time invariant (LTI) systems. If this material is new to you, read what follows carefully and use the references to fill in any blanks you find; if this stuff is old hat, then give it a passing glance, if for no other reason than to familiarize yourself with the notation found throughout the book. 3.1 Random Variables First, I'll briefly review random variables, limiting my discussion to continuous random variables. 3.1.1 Definitions First, as usual, some definitions. A random event, A, refers simply to an event with an unknown outcome. An example of a random event is tomorrow's weather. Next, a random variable, x, is a number whose value is determined by a random event, A. For example, it may be tomorrow's outdoor temperature in Fort Collins, Colorado (where I live). 3.1.2 The Distribution Function: One Way to Describe X Let's say you've got a random variable, x, which is tomorrow's temperature. You want to somehow be able to describe x = (tomorrow's temperature) to someone. You don't know exactly what this value will be, but you do know it's the middle of summer, SO you know it's a lot more likely to be 80 degrees (Fahren