Over the next few weeks we will direct our efforts towards a consolidation of the key concepts encountered in your previous study of random variables. This is important since one of our aims in this course is to incorporate a temporal dimension into your understanding. The assignment you have just completed begins to do this since it is hopefully apparent that we can model random noise on a signal using a random number generator. It turns out of course that when we sample or measure a signal that is corrupted by noise, we are measuring a random variable. In some cases we may well obtain sampled data with familiar, well-defined statistical properties. At least this is our hope.
Figuring out how to do this is the problem of course and we’ll use a combination of reading (I know how you all love our textbook!), discussion and simulation studies to try to achieve this goal. To make this manageable, the web-notes for the course provide a summary presentation of what I believe to be the key concepts you should be comfortable with. We’ll review these during our class times. In addition, I have identified key sections of the textbook that I think you should read. These do not cover all of the important ideas of course. (You can never predict when some obscure result or property provides the answer to some real problem.) These readings are,
Chapter 2. Sections 2.8, 2.11, 2.12
Chapter 3. Sections 3.2, 3.3, 3.5
Chapter 4. Sections 4.1, 4.2
Assigned work for week beginning, Friday 4th September, 1998.
Read the assigned sections in chapter 2 of the textbook. As you read, note any questions you have about this material. Review the web-notes on Axiomatic Probability. If you can answer the questions in the notes I think we are ready to move on. If not, try to find the answers in the textbook. If you get really desperate, send me an e-mail with your questions.
To prepare for our discussions next Friday, take some time to "play with" the MATLAB m-files binom.m and gauss.m [You can copy these from the ftp site for the course.] It should not take much more that 30 minutes. Vary the statistical parameters for each of the pdfs and plot/print a few representative results. Make a note on your results of the specific values of the pdf’s parameters such as p, q, m x and s x. Bring these results to class with you.
With your study partner, if you choose to have one, identify the topic you intend to research for your course paper. E-mail me this information by next Wednesday, 9th September.
If you have some additional time to devote to the cause, review the next set of web-notes on Probability Density and Distribution Functions.
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