How to understand and reason about risk and uncertainty

You will rapidly reconnect expected value to real decisions, exposing its hidden assumptions so you can see exactly where it breaks down under uncertainty.

You will characterize uncertainty using probability distributions and identify how fat tails and rare but catastrophic events systematically mislead expected-value reasoning.

You will apply Bayes' theorem to revise beliefs as evidence arrives, distinguishing model uncertainty from parameter uncertainty and avoiding common prior-choice pitfalls.

You will combine distributional thinking and Bayesian inference into a unified framework for making robust, well-calibrated decisions when both data and models are uncertain.