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Fix equation terms in diffusion.jl (#22)
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Lectures/diffusion.jl

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -53,9 +53,9 @@ f_Y(y)
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& = \int_x \frac{x-y}{\sigma^2} f_{X,Y}(x,y) \, \text{d} x\\
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\sigma^2 \nabla_y f_Y(y)
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& = \int_x x f_{X,Y}(x,y) \, \text{d} x - y \int_x f_{X,Y}(x,y) \, \text{d} x\\
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& = \int_x x f_{X|Y}(x|y) \, \text{d} x f_{Y}(y) - y\\
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& = \int_x x f_{X|Y}(x|y) \, \text{d} x f_{Y}(y) - y f_{Y}(y)\\
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\sigma^2 \nabla_y f_Y(y) / f_{Y}(y)
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& = \mathbb{E}[X | Y = y] - y f_{Y}(y)\\
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& = \mathbb{E}[X | Y = y] - y\\
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y + \sigma^2 \nabla_y \log f_Y(y) & = \mathbb{E}[X | Y = y].
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\end{align*}
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```

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