This is the final exam for Fat Tails & Black Swans. It pulls the whole course together: the two worlds (mild Mediocristan vs. wild Extremistan), the bell curve and the power laws that mock it, the many ways the average lies when tails are fat, the black swan and its mascot the doomed turkey, and finally ergodicity — why a bet that’s great on average can still ruin you. Several questions look easy until you notice a Gaussian assumption hiding in the weeds, or a “positive expected value” that quietly leads to zero. Reason each one through.
How this exam works
Read carefully — this exam is final. Each question appears one at a time. Once you submit an answer it is locked for good: there’s no going back, no retry, and no restart. Your score is hidden until the end, where you’ll see a pass/fail verdict. The pass mark is 70%. A few questions ask you to select all correct answers.
What is the single cleanest test for telling whether a quantity lives in Mediocristan or Extremistan?
Select an answer to continue.
Course Recap
Big picture
Fat tails & black swans, in one picture
- Fat Tails & Black Swans
- Mediocristan vs Extremistan
- Ask: can one observation dominate the total? Height is mild & non-scalable (Mediocristan); wealth is wild & scalable (Extremistan). A mean far above the median signals the wild world.
- Bell curve vs power laws
- Gaussian tails die super-exponentially (68-95-99.7), so they call real crashes "10-sigma impossible." Power-law tails P(X>x) ~ x^(−alpha) decay slowly; smaller alpha = fatter tail; 80/20 nests to ~64/4.
- When the average lies
- With alpha ≤ 1 the mean is infinite and never settles; one giant point dominates mean and variance; the median is more honest; finite backtests under-represent the tail, so "never happened" proves nothing.
- Black swans & the turkey
- Outlier + extreme impact + hindsight predictability. The turkey is most confident the day before slaughter (problem of induction). Absence of evidence ≠ evidence of absence; build robustness, not forecasts.
- Ergodicity & ruin
- Time average ≠ ensemble average: the +EV flip 1.5 × 0.6 = 0.9 still ruins you. With an absorbing barrier at zero, ruin creep 1 − (1 − p)^n nears certainty. Barbell, margin of safety: survive first, optimize second.
- Mediocristan vs Extremistan
Key takeaways
Fat-tailed thinking starts by asking which world you are in: in Mediocristan no single observation can move the total, while in Extremistan one giant can swamp everything — and a mean sitting far above the median is your tell. The bell curve crushes its tails super-exponentially, which is why a Gaussian model brands real crashes “impossible,” whereas power laws decay only polynomially and keep extremes alive (smaller alpha, fatter tail; 80/20 nesting to ~64/4). Once tails are fat, the average lies: it can be infinite, hostage to the single largest point, and systematically under-counted by any finite backtest — so “it has never happened” is a statement about your sample, not the world. That is the soil where black swans grow (outlier, extreme impact, hindsight-predictable), and where the turkey feels safest the day before slaughter. The deepest lesson is ergodicity: a bet that is great on average can still ruin you, because wealth compounds through time (1.5 × 0.6 = 0.9), and once you hit the absorbing barrier at zero there is no coming back. So build a barbell, keep a margin of safety, and remember the rule beneath all of it — survive first, optimize second.