Probability and Statistics

Mathematics for Materials and Design

The full set of notes for this topic is here. All materials on this topic can be downloaded here.

Sessions:

1. Elementary probability
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction.
     • Venn diagrams example.
     • Multiple events.
     • Probability trees.
     • The Monty Hall problem.


2. Exploratory data analysis and statistics
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction.
     • Centrality I.
     • Centrality II.
     • Dispersion.
     • EXCEL histograms.
     • EXCEL stats functions.


3. Probability distributions
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction and probability distributions.
     • The normal distribution.
     • Normal distributions - example 0.
     • Normal distributions - example 1.
     • Normal distributions - example 2.
     • The log-normal distribution.


4. Combining distributions and Chauvenet's criterion
   • Lecture materials: slides and handout, the starting point of the Chauvenet's criterion example and the result.
   • Additional resources: Example of applying Chauvenet's criterion.
   • Videos:
     • Introduction.
     • Combining probability distributions.
     • Example of combining normal distributions.
     • Chauvenet's criterion.
     • Example of Chauvenet's criterion.
     • Extra example of combining normal distributions.


5. Curve fitting and correlation
   • Lecture materials: slides and handout. See also each stage of the lecture example - part 1, part 2 and part 3.
   • Additional resources: demonstration of curve fitting for Covid-19 case data in the UK.
   • Videos:
     • Introduction.
     • Curve fitting.
     • Example of curve fitting using EXCEL.
     • The R-squared value.
     • Example of the R-squared value.
     • Example of calculating the R-squared value using EXCEL.
     • Application to modelling COVID-19.
     • Guide to plotting graphs of functions in EXCEL.


6. Discrete probability distributions
   • Lecture materials: slides and handout.
   • Videos:
     • Introduction.
     • Binomial distributions.
     • Example of binomial distributions.
     • Poisson distributions.
     • Example of poisson distributions.