The interactive film is in the book's Companion

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Conditional Gaussian: A Slice of the Bell

Chapter 13 · Mathematics for AI and Machine Learning · Beginner · 1:40

An interactive live film: a wall at Y = y cuts the bell of a 2D Gaussian in 3D; the cut is the Gaussian of X given y, its peak riding the regression line while its width stays fixed; the reader slides the wall and changes the correlation.

Narration

Two jointly normal variables, X and Y, have this bell shaped density over the plane. Their correlation tilts the bell along the diagonal.

Now condition on Y equal to y. Stand a wall at that value, and cut the bell. The cut, in pink, is the shape of X given Y equals y.

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

More from Chapter 13

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