14.4 Demos Glossary

Chapter 1 - Probability Fundamentals¶

Chapter 2 - Random Variables and Distribution Functions¶

1. Distribution Plotter. This is the tool used in Sections 2.2 and 2.4 to visualized PMFs and PDFs. You will need it for your first HW. It is a good reference to come back to throughout the course. I suggest you bookmark it.

2. Dartboard Sampler - This is the example used in Section 2.3 to derive the idea of a density function.

3. PMF, PDF, CDF Explorer -This the tool used in Sections 2.1, 2.2 and 2.4 tp visualize the relationship between the PMF, CDF, and PDF.

Chapter 3 - Visualizing Functions and Models¶

1. Function Properties and Linear Transformations - Use this tool to visualize linear transformations of functions (inputs and outputs) and to check your understanding of key global properties.

2. Function Combination - Use this tool to visualize linear combinations and products of functions.

3. Function Composition I - 2D - Use this tool to visualize function compositions.

4. Function Composition II - 3D - Use this tool to visualize function compositions in three dimensions. It works best when the outer function is monotonic and bounded.

5. Function Inversion - Use this tool to visualize function inverses.

Chapter 4 - Summarizing Distributions with Expectations¶

1. Law of Large Numbers Interactive - Use this interactive to watch sample averages over large data sets converge to expectations.

Chapter 5 - Comparing Tails¶

1. Tail Visualizer - Use this tool to visualize tails on log scales.

Chapter 6 - Function Approximation¶

1. Taylor Series Visualizer - Use this tool to visualize Taylor series.

Chapter 7 - Integration Techniques¶

1. Change of Density Visualizer - Use this tool to visualize changes of density.

Chapter 8 - Random Vectors¶

1. Surface Visualizer - Use this tool to visualize surfaces.

2. Probability as Volume Visualizer - Use this tool to visualize probabilities as volumes under a joint distribution.

Chapter 9 - Derivatives of Multivariate Functions¶

1. Gradient Visualizer - Use this tool to visualize the gradient vector fields associated with a surface.

2. Gradient Ascent Visualizer. - Use this tool to visualize gradient ascent on the same surfaces provided in the Gradient Visualizer.

3. Least Squares Visualizer - Use this tool to visualize the mean square error objective function used in least squares regression.

Chapter 10 - Integrals of Multivariate Functions¶

1. Probability as Volume Visualizer - Use this tool to visualize probabilities as volumes under a joint distribution.

2. Conditional Expectation Visualizer - Use this tool to visualize conditional expectations.

3. Convolution Visualizer - Use this tool to visualize convolutions.

Chapter 11 - Measuring Association¶

Chapter 12 - Estimation¶

Chapter 13 - Concentration¶

1. Law of Large Numbers Interactive - Use this interactive to watch sample averages over large data sets converge to expectations.

2. Convolution Visualizer - Use this tool to visualize convolutions.

3. Distribution Plotter. - Use this tool to visualize densities and to experiment with limiting distributions.