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Probability and Random Variables

Under development

This lesson is part of the course scaffold and is being actively written. The learning objectives and outline below define its final scope.

Learning objectives

By the end of this lesson you will be able to:

  • Frame trading questions as probability statements and compute conditional probabilities of market events (for example, the probability of a down day given a prior drawdown) from historical data.
  • Model market quantities as discrete and continuous random variables and select an appropriate model for a given quantity.
  • Estimate the first four moments of a daily return series, attach standard errors, and interpret skewness and kurtosis in trading terms.
  • Quantify dependence between assets using covariance, Pearson correlation, and rank correlation, and demonstrate on real data where linear correlation misleads.

Outline

  1. Probability in a trading context — events, conditioning, and base rates
  2. Random variables — discrete and continuous models of market quantities
  3. Moments — mean, variance, skewness, and kurtosis of real return series
  4. Estimating moments — sample estimators, standard errors, stability across periods
  5. Dependence — covariance, correlation, rank correlation on asset pairs
  6. Beyond linear correlation — tail dependence and correlation breakdown in stress
  7. Case study — moments and dependence across major asset classes

Prerequisites