I am trying to understand various types of stochastic processes. In order for that to happen, I needed some simple examples to be built so that I can build an intuition about them.

According to the book of Hwei Hsu (Chapter-5, Page-161, "Description of a Random Process"), I can design the following simple and intuitive examples myself using only a standard die:

1. Discrete-parameter (or Discrete-time) process
3. Discrete-state process (or a Chain)

Suppose, we roll a die either a finite ($n$) number of times or an infinite number of times and plot them as a graph like the following:

enter image description here

Are my examples correct? If not, kindly help me to make the necessary corrections.


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