Every risk report, backtest summary, and pricing expectation is a statement about a random variable — a return, a loss, a default indicator — and about how that random variable behaves jointly with others. This topic rebuilds the university language of probability from that job: distributions and moments, dependence, conditioning, and the limit theorems that justify treating a sample mean of returns as concentrated and a sum of risks as approximately normal. It assumes the Mathematics Primer floor and goes straight to the formalism research, risk, and econometrics use every day.
By the end of this note you should be able to:
- work fluently with PMFs, PDFs, CDFs, expectation and variance for discrete and continuous laws used in finance;
- read joint distributions, covariance, and correlation, and separate correlation from dependence;
- treat conditional expectation as a random variable and apply the tower property;
- state the weak (and strong) law of large numbers and the central limit theorem with hypotheses, and know where they fail for financial data.
In this lesson
- Contents
- The big picture
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