The interactive film is in the book's Companion

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Independence as an Outer Product

Chapter 13 · Mathematics for AI and Machine Learning · Beginner · 1:38

An interactive live film: a 3x3 joint table as bars, its marginals as shadows on two walls; independence makes the table the rank-one outer product of the shadows. Move mass without moving the shadows and make X and Y uncorrelated but still dependent.

Narration

Two variables, X and Y, each taking the values zero, one and two. Their joint distribution is a three by three table of probabilities, drawn as bars on the floor.

Summing each row gives the marginal of X, the shadow on the left wall. Summing each column gives the marginal of Y, the shadow on the back wall.

The rest of the narration is in the book's Companion.

More from Chapter 13

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