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[odu] FIX: reformat wide equation (#413)
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* FIX: reformat wide equation

* taking the and out of latex math for improved formatting
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mmcky authored Oct 2, 2024
1 parent 1a42a80 commit 37f7eae
Showing 1 changed file with 10 additions and 2 deletions.
12 changes: 10 additions & 2 deletions lectures/odu.md
Original file line number Diff line number Diff line change
Expand Up @@ -167,7 +167,11 @@ $$
\mathbb{P}\{q = f \,|\, W = w\}
= \frac{\mathbb{P}\{W = w \,|\, q = f\}\mathbb{P}\{q = f\}}
{\mathbb{P}\{W = w\}}
\quad \text{and} \quad
$$

and

$$
\mathbb{P}\{W = w\} = \sum_{\omega \in \{f, g\}} \mathbb{P}\{W = w \,|\, q = \omega\} \mathbb{P}\{q = \omega\}
$$

Expand All @@ -178,7 +182,11 @@ Letting

$$
q_{\pi}(w) := \pi f(w) + (1 - \pi) g(w)
\quad \text{and} \quad
$$

and

$$
\kappa(w, \pi) := \frac{\pi f(w)}{\pi f(w) + (1 - \pi) g(w)}
$$

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