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Mathematics Primer / Probability and Statistics

Probability Fundamentals

A loss probability needs a clear definition of the loss, the time horizon and the conditions being considered. This lesson defines outcomes and events, then shows how probabilities change when you receive information. Those steps prepare you to calculate expected return and variance and read a normal risk model.
Learning objectives. By the end of this note you should be able to:
  • define a sample space and event for a simple financial experiment;
  • apply complements, unions and intersections;
  • use the probability axioms and addition rule;
  • compute a conditional probability and apply Bayes' rule;
  • distinguish independence from mutual exclusivity.

In this lesson

  1. Outcomes, events and probability
  2. Conditioning updates the relevant universe
  3. Independence is not disjointness
  4. Conditioning changes the denominator

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