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Random Variable Concept Map

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About This MicroSim

This interactive concept map shows how all the random variable concepts from Chapter 13 fit together. Click on any node to see its definition, and drag nodes to rearrange the layout for better viewing.

The map is color-coded:

  • Green (Core Concepts): Fundamental definitions like Random Variable, Expected Value
  • Auburn (Formulas): Calculation methods and mathematical relationships
  • Brown (Distributions): Specific probability distributions (Binomial, Geometric)

How to Use

  1. Click any node to see its definition in the info panel
  2. Click the same node again and drag to rearrange the layout
  3. Follow the edges to understand how concepts relate to each other
  4. Click elsewhere to close the info panel

Concept Relationships

The map shows several key relationships:

From Random Variable

  • Random Variable is a type of Discrete RV (we focus on discrete in this chapter)
  • Random Variable has a Probability Distribution
  • Random Variable is summarized by Expected Value E(X)

From Expected Value

  • Expected Value spread by Variance
  • Expected Value changes via Linear Transformation

From Variance

  • Variance sqrt gives Standard Deviation
  • Variance combines via Combining RVs rules

Special Distributions

  • Discrete RV has special cases: Binomial and Geometric Distributions
  • Each has its own formulas for probability, mean, and standard deviation

Learning Objectives

After using this MicroSim, you'll be able to:

  • Organize your understanding of random variable concepts
  • Trace the connections between definitions, formulas, and distributions
  • See the "big picture" of Chapter 13
  • Identify prerequisite knowledge for each concept

Using the Map for Review

Before an Exam

  1. Start at "Random Variable" and work outward
  2. For each node, ask yourself: "Can I explain this concept?"
  3. Quiz yourself on the formulas in auburn nodes
  4. Make sure you can distinguish Binomial from Geometric settings

For Problem Solving

  1. Identify which concepts are relevant to your problem
  2. Trace the path from the given information to what you need to find
  3. Use the formulas along the way

Sylvia Says

"A concept map is like a bird's-eye view of the forest. Instead of getting lost among the trees (individual formulas), you can see how everything connects. When you're stuck on a problem, the map can help you find a path from what you know to what you need!"

Embedding This MicroSim

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<iframe src="https://dmccreary.github.io/statistics-course/sims/random-variable-concept-map/main.html" height="502px" scrolling="no"></iframe>

Technical Notes

  • Built with p5.js 1.11.10
  • Uses pre-calculated node positions with force-directed aesthetic
  • Nodes are draggable for custom layouts
  • Responsive width design
  • Canvas height: 500px

References

  • Chapter 13: Random Variables
  • All 23 concepts from the chapter are represented in this map