What's Next?

Continue Your Probability Journey

Deeper Probability

  • Stochastic processes — Brownian motion, Poisson processes, martingales, and stopping times.
  • Measure-theoretic probability — the rigorous foundation: sigma-algebras, Lebesgue integration, and the Radon-Nikodym theorem.
  • Bayesian statistics — PyMC or Stan for probabilistic programming and posterior inference.

Applied Directions

  • Machine learning — probabilistic graphical models, variational inference, and generative models (VAEs, diffusion).
  • Quantitative finance — stochastic calculus (Itô's lemma), Black-Scholes, and the Options Pricing course.
  • Information theory — entropy, mutual information, and the channel capacity theorem.

References

  • Introduction to Probability by Blitzstein & Hwang — the best modern probability textbook, with solved problems and intuition.
  • Probability Theory: The Logic of Science by E.T. Jaynes — Bayesian perspective, free online.
  • 3Blue1Brown: Bayes Theorem — visual intuition for conditional probability.
  • Harvard Statistics 110 — Blitzstein's full course with lecture videos and problem sets, free online.
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