Statistics
Statistics questions test whether you can summarize data, estimate parameters, and avoid fooling yourself with noise — the daily work of a quant researcher.
Lessons · recommended order
- 1Mean, Variance and CovarianceThe core summary statistics of a distribution: variance measures spread, covariance measures co-movement, correlation normalizes it.Foundations9 min
- 2Law of Total ExpectationE[X] = E[E[X|Y]]: decompose an expectation by conditioning on a variable that splits the problem into tractable cases.Foundations6 min
- 3Law of Total VarianceVar(X) splits into an average within-group variance plus the variance of the group means: within-group + between-group.Intermediate8 min
- 4Maximum Likelihood EstimationChoose the parameter that makes the observed data most probable by maximizing the (log-)likelihood function.Intermediate10 min
- 5Bayesian Updating with Conjugate PriorsA Beta(a,b) prior on a probability updates to Beta(a+successes, b+failures) after observing Bernoulli data.Intermediate9 min
- 6Simple Linear RegressionThe least-squares slope is Cov(X,Y)/Var(X); residuals are the leftover variation regression fails to explain.Intermediate9 min
- 7Multiple Testing and False DiscoveriesTesting many hypotheses at once inflates the chance of a false positive; Bonferroni correction controls it at the cost of power.Intermediate8 min
- 8Time-Series Validation and Walk-Forward TestingRandom cross-validation leaks future information in time series; walk-forward validation respects the arrow of time.Intermediate7 min