Continuous-state vs. Discrete-state process

          The value of a random process is at any time can be described from its probabilistic model.

          The state is the value taken by at a time , and the set of all such states is called the state space. A random process is discrete-state if the state-space is finite or countable. It also means that the corresponding sample space is also finite or countable. Otherwise , the random process is called continuous state.

Example 4 Consider the random sequence generated by repeated tossing of a fair coin where we assign 1 to Head and 0 to Tail.

Clearly, can take only two values - 0 and 1. Hence is a discrete-time two-state process.