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# System prepended metadata

title: Untitled

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### Probabilistic Model:
$X \rightarrow Y \rightarrow Z$

e.g. 
-"clouds" (X) cause "rain" (Y)
-"rain" (Y) causes "water in bucket" (Z)

$X = N_1$
$Y = \alpha_1*X + N_2$
$Z = \alpha_2*Y + N_3$
where $N_i \sim N(0,\sigma_i^2)$

### Inference:
Given: observations $\{ x_i, y_i, z_i \}_{1,...,n}$
Goal: find a model to predict $Y$

