This notebook is the compact review layer for the full math section. It reconnects the main ideas through short business examples so the formulas stay anchored to practical interpretation.## Quick Reference| Topic | Formula | Business reading || --- | --- | --- || Mean | $\mu = \frac{1}{n}\sum x_i$ | average KPI || Linear model | $y = \beta_0 + \beta_1x$ | baseline plus effect || Derivative | $\frac{dy}{dx}$ | local sensitivity || Expected value | $E[X] = \sum P(x)x$ | average payoff under risk || Bayes rule | $P(A \mid B) = \frac{P(B \mid A)P(A)}{P(B)}$ | update belief with evidence |## Worked Example Set- Forecast: if $y = 5000 + 3x$ and $x = 1000$, predicted sales are 8000- Optimization: if $R(p) = p(100 - 2p)$, setting the derivative to zero gives $p = 25$- Expected value: combining uncertain outcomes yields an average payoff even when no single outcome is guaranteed- Churn probability: total probability combines multiple customer paths into one overall risk estimatemermaidflowchart TD A[Notation] --> B[Linear model] --> C[Optimization] --> D[Probability] --> E[Decision]Alt text: The cheat-sheet connects math ideas into one decision-making chain.## Quick Check1. What is the predicted outcome if $y = 4000 + 2x$ and $x = 500$?2. What is the expected value of a payoff of 100 with probability 0.3 and 0 otherwise?3. What do you usually inspect after finding a zero derivative?