Statistics & Distributions
Distributions, estimation, hypothesis testing, regression, and signal detection for quantitative finance.
Course Lessons
Normal Distribution & LLN
The bell curve, z-scores, the 68-95-99.7 rule, and the law of large numbers
Continuous Distributions
Uniform, exponential, and log-normal — and when to use each
Central Limit Theorem
Why the normal distribution is everywhere
Gamma & Beta Distributions
Gamma, chi-squared, Beta distributions, and Bayesian conjugate priors
Estimation & Sharpe Ratio
Point estimation, bias-variance tradeoff, and risk-adjusted returns
Hypothesis Testing
p-values, t-tests, Type I/II errors, and statistical significance
Correlation & Covariance
Measuring relationships between assets, beta, and diversification
Maximum Likelihood Estimation
Fitting distributions and estimating parameters from data
Confidence Intervals
Constructing and interpreting intervals for means and proportions
Linear Regression
OLS, factor models, residual analysis, and R-squared
Information Theory
Entropy, KL divergence, mutual information, and applications to quant finance
Multivariate Normal
Joint PDFs, bivariate normal, conditional distributions, and Cholesky simulation
Bayesian Inference
Conjugate priors, posterior updating, credible intervals, and Bayes factors
Regression & Regularization
Multicollinearity, heteroscedasticity, Ridge/Lasso, and cross-validation
Time Series — ARIMA
Stationarity, AR/MA models, ARIMA, and Box-Jenkins methodology
Principal Component Analysis
Eigendecomposition, factor extraction, yield curve PCA, and covariance denoising
Moving Averages & Signals
Crossover strategies and trend detection
Time Series — GARCH
Volatility clustering, GARCH(1,1), and conditional variance forecasting