This is the capstone. Six lessons assembled the statistical spine of quantitative finance — how randomness is described by probabilities, PMFs, PDFs and CDFs; the distributions returns actually follow and the fat tails that wreck the bell curve; the moments that summarize a distribution; how two assets co-move and how a regression line estimates beta; why averages go normal and what a standard error really measures; and how to test a claim without fooling yourself. No formula sheet, no hints, no take-backs: every answer locks the instant you submit, the wrong options are the exact traps that sink real research desks, and your score stays hidden until the end.
How this exam works
This is a graded exam. Questions arrive one at a time. Once you submit an answer it is final — there is no going back, no second try, and a wrong answer simply fails that question. Your score stays hidden until the very end, where you need 70% to pass. Read every option before you commit.
For two questions you will need the small dataset below.
| Day | Asset A return | Asset B return |
|---|---|---|
| 1 | +2% | +1% |
| 2 | −1% | 0% |
| 3 | +3% | +2% |
| 4 | 0% | −1% |
A fair six-sided die is rolled once. What exactly is the 'sample space' of this experiment?
Select an answer to continue.
Whatever the score reads, the chain you just stress-tested — probability, distributions, moments, regression, sampling and inference — is the literacy every quant course leans on. Here is the entire topic in one glance.
Course Recap
Big picture
The Statistics-for-Finance Toolkit
- Statistics for Finance
- Probability & random variables
- Sample space, events, conditional probability
- Independence = joint equals product of marginals
- PMF (discrete), PDF & CDF (continuous)
- Expectation = probability-weighted average payoff
- Distributions in finance
- Normal & the 68–95–99.7 rule; z-scores
- Lognormal prices, additive log returns
- Fat tails: normal underestimates extremes
- Student-t for heavy tails; skew = asymmetry
- Expectation, variance & moments
- Mean, variance, standard deviation
- Sample variance divides by n minus 1 (unbiased)
- Annualize volatility by the square root of time
- Skewness (asymmetry), kurtosis (tail heaviness)
- Covariance, correlation & regression
- Covariance sign = same-side vs opposite moves
- Correlation bounded in negative 1 to positive 1
- OLS slope is beta; intercept is alpha
- R squared = variance explained; corr is not causation; linear only
- Sampling, CLT & estimation
- Sampling distribution of a statistic
- CLT: the sample MEAN goes normal
- Standard error = sigma over root n (4x data to halve)
- Unbiased vs consistent; MLE; confidence-interval meaning
- Hypothesis testing
- Null (no effect) vs alternative; t-statistic
- p-value = P(data this extreme | null is true)
- Type I (false positive) vs Type II (false negative); power
- Multiple testing / data snooping; significance is not economic relevance
- Probability & random variables
Key Takeaways
What you now own
Returns are random variables, risk is a standard deviation, and an edge is a coefficient you have to prove is real. You can read a probability off a CDF, standardize a move into a z-score, and explain why fat tails make the normal lie about crashes. You know the sample variance divides by n minus 1, that volatility scales with the square root of time, and that a regression slope is beta while R-squared is variance explained — and that correlation is never causation. You can state the Central Limit Theorem correctly (it is the mean that goes normal), shrink a standard error by quadrupling the data, and read a confidence interval without claiming it is a 95% probability about the parameter. Above all, you can read a p-value as P(data this extreme | null true) — not the probability the null is true — and you respect the data-snooping trap that turns a thousand backtests into a guaranteed false positive. That is the statistical spine every expert quant course hangs from.