I finished a set of background notes for the uncertainty quantification class (ME470) I’m teaching this quarter with Gianluca Iaccarino. A link to the notes is below. Let me know if you think I left anything out (or if you find any typos)!

ME470 background notes

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It seems there is a typo in the definition of convergence in probability.

Thanks, Ivan! I’ve fixed that along with a typo in the almost sure convergence.

Nice notes. I would suggest adding to Section 1.7 that the median and quartiles are also commonly used summary statistics, and have nicer robustness properties in the presence of outliers than the mean and standard deviation. So, for example, (Q3-Q1)/Q2 is a “better” normalized measure of spread than $\sigma/\mu$.