PHYS 10471: Random Processes in Physics

Prof. R.M. Jones, University of Manchester

Essential Preliminaries

Lectures take place on Wednesday at 9 am in the Simon Lecture Theatre B and also on Friday at 1 pm in Theatre B of the Simon building.

An examples class will also take place on Friday at 2 pm in Theater B of the Simon building.

The course syllabus covers 5 sections: 1. Elements of probablity, 2. Probability distributions, 3. Exponential probablity distribution, 4. Poisson probability distribution, 5. Binomial distribution

Recommended books for the course include:

Chapter 39 and 40 of Mathematical Techniques. 3rd Ed., Jordan, D. and Smith, P.
Chapter 20 and 21 of Mathematics for Engineers and Scientists, Weltner, K., Gorsjean, J., Schuster, P., and Weber, W.
Chapter 3 of Statistics, Barlow, R.J

Please note that there is no mid-semester assessment. This course unit is assessed by examination at the end of the semester, in January. However, I will distribute a mid-semester feedback test that is entirely for your own benefit. You may take it in your own time, under timed exam conditions, or not, open book, or not, as you prefer. Your grade is only to give you feedback on how you are doing, so you will know how to interpret it in relation to how you did the test.

The course is assessed with a 1 hr 30 min examination in January (three questions should be answered out of four, the first of which is compulsory)

Elements of Probability

Lecture 1: summary, Lecture 2: summary, Mathematica notebook: Birthday.nb

Lecture 3: summary, Lecture 4: summary

Lecture 5: summary, Lecture 6: summary Mathematica notebook: Coin Toss.nb

Lecture 7: summary, Mathematica notebook: Gaussian.nb, Lecture 8: summary, Mathematica notebook: Self_Convolution.nb, Top_Hat_Distribution.nb

Lecture 9: summary, Mathematica notebook: ExpFunction.nb, Lecture 10: summary

Lecture 11: summary, Lecture 12: summary

Lecture 13: summary, Lecture 14: summary

Lecture 15: summary, Lecture 16: summary, Mathematica notebook: PoissonFunction.nb,

Lecture 17: summary, Lecture 18: summary

Lecture 19: summary, Lecture 20: summary, Mathematica notebook: Binomial.nb

Lecture 21: summary, Lecture 22: summary

Examples

Sheet 1 (Proof of Vandermonde's identity)

Sheet 2 (Properties of Hypergeometric distribution)

Sheet 3

Sheet 4

Sheet 5

Exam Questions

2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 (BLA)

Additional papers and "bottom line" solutions are available on the student Blackboard (moved from teachweb).

Unless indicated otherwise, the materials are in Adobe pdf format. An Adobe reader is necessary to open these materials and can be obtained (at no cost) here. Powerpoint (ppt) and Mathematica (nb) files are also available for download. You can either download a full stand-alone version of Mathematica or VPN to the university (details are here). These notebooks are written in Mathematica 11 (or higher). Please notify me of any errors you find. Comments and suggestions are welcome. Acknowledgement: this material is based on earlier lectures of Prof. M. Seymour, Dr. M. Godfrey and Dr. A.C. Philips. My e-mail address is roger.jones@manchester.ac.uk