Visual Anchors Plan

The concepts presented across the chapters of the “Stats 2 book” lend themselves well to concrete visual illustrations. We are moving beyond static images to interactive Astro components.

1. Basic Probability (Chapter 1)

Goal: define fundamental vocabulary (Sample Space, Outcome, Event).

Anchor	Concept	Implementation
	Sample Space ($S$)	Use 3D dice to show $S=\{1..6\}$.
H T	Binary Outcomes	Flipping coins for $P(H)=0.5$.

2. Sampling & Repeated Trials (Chapter 2)

Goal: Emphasize repetition and replacement.

Anchor	Concept	Implementation
Repetitive Flips	Bernoulli Trials	Sequences of H T to show Binomial/Geometric patterns.
	Sampling Dependence	Urn schemes for Hypergeometric distribution (Sampling without replacement).

3. Discrete Random Variables (Chapter 3)

Goal: Shift from concrete outcomes to numerical functions.

• Multi-Flip Coin Table: Mapping outcomes ($hhh \to 3$) using tables.
• Convolution: Using multiple dice
  +
  to explain summing random variables.

4. Continuous Distributions (Chapters 4-7)

Goal: Visualizing density and spread.

5. Relationships & Testing (Chapters 6-10)

Goal: Decisions based on data.

• Bivariate Density: Visualizing Correlation.
• Regression Lines: Least Squares fit.
• Z-Test Area: Using the Normal Curve tail areas to explain P-values.