One of the first concepts covered in the course, as you may have guessed, is random walks. And no I am not talking about taking a spontaneous stroll to an unknown destination. Loosely defined, a random walk is an infinite sequence of positive and/or negative steps. It is important to introduce this concept early in the course because many other statistical concepts rely on understanding a random walk (e.g. – random variables, expectations, independence, etc.). Remember, that this course develops statistical concepts using a theoretical framework. So although you may have previously encountered random variables and expectations, they are more rigorously defined through aspects of random walks.
This section of the online supplement provides the following materials: a video about random walks, a practice problem, and the R code used to generate the figures in the video. The video covers the following:
- description of a random walk
- some notation
- a step-by-step solution to a random walk problem
- in-video questions to check for understanding (be sure to carefully read the questions, some of them require you to type out a numerical answer, i.e. – you would need to type out “zero” not “0” – without the quotation marks)
The practice problem is actually a sub-proof to the problem discussed in the video. Therefore it is highly encouraged that you watch the video first, then attempt the practice problem. If you would like to just see the practice problem (without the solution), so you can try working through it yourself, click here. The solution to the practice problem is also provided here. The proof toolkit tab may be helpful with solving the problem.
The code used in the video is available to download here. (You will be redirected to a Google Drive platform, just click the “Download” button).