| Expected value | Expected return, risk-neutral pricing (option price = discounted expected payoff) | Population mean, conditional expectation E[Y|X], the target of regression |
| Variance, σ√n | Volatility, portfolio risk, diversification | Standard errors shrink with √n; this is why sample size matters |
| Linearity | Portfolio return = weighted sum of asset returns | OLS: Y = β₀ + β₁X + ε, linear in parameters |
| Conditional EV updates | Prices react to news; efficient-market hypothesis | Conditioning on controls; omitted-variable bias when you don't |
| Bayes in odds | Updating forecasts, credit default models | Bayesian estimation, logistic regression (log-odds are linear) |
| Kelly sizing | Position sizing, leverage, the Sharpe ratio | Maximising expected log utility; geometric vs arithmetic mean |
| Adverse selection | Bid-ask spread theory (Glosten–Milgrom, Kyle) | Selection bias, endogeneity |
| Calibrated intervals | Value at Risk, confidence in forecasts | Confidence intervals and hypothesis tests |
| Monte Carlo equity | Monte Carlo option pricing | Bootstrap, simulation-based inference |