TABLE OF CONTENTS A random process or stochastic process is a family of random variables. In principle this could refer to a finite family of random variables such as { X, Y, Z}, but in practice the term usually refers to infinite families. The need for working with infinite families of random variables arises when we have an indeterminate amount of data to model. For example, in sending bits over a wireless channel, there is no set number of bits to be transmitted. To model this situation, we use an infinite sequence of random variables. As another example, the signal strength in a cell-phone receiver varies continuously over time in a random manner depending on location. To model this requires that the random signal strength depend on the continuous-time index t. More detailed examples are discussed below.
A discrete-time random process is a family of random variables { X n} where n ranges over a specified subset of the integers. For example, we might have
Recalling that random variables are functions defined on a sample space ?, we can think of X n( ?) in two ways. First, for fixed n, X n( ?) is a function of ? and therefore a random variable. Second, for fixed ? we get a sequence of numbers X 1( ?), X 2( ?), X 3( ?),
