deletions | additions       diff --git a/begin_align_P_y_i_1__.tex b/begin_align_P_y_i_1__.tex  index 5a3b443..4d4174b 100644  --- a/begin_align_P_y_i_1__.tex  +++ b/begin_align_P_y_i_1__.tex 
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\begin{align}  P(y_i = 1 \| \mathbf{X}) \mid \mathbf{w, x_i})  &= \sigma(\mathbf{w^T x_i)\\ x_i})\\  \\ P(y_i = 0 \| \mathbf{X}) \mid \mathbf{w, x_i})  &= 1 - \sigma(\mathbf{w^T x_i})\\ &= \sigma(\mathbf{-w^Tx_i})  \end{align}