deletions | additions       diff --git a/begin_align_p_y_i_1__.tex b/begin_align_p_y_i_1__.tex  index 70995cb..7d0fffc 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 \mid \mathbf{x_i}) &= \sigma(\mathbf{w^T x_i})\\ \\  p(y_i = 0 \mid \mathbf{x_i}) &= 1 - \sigma(\mathbf{w^T x_i})\\  &= 1 - \frac{1}{1 + \exp (- \mathbf{w^Tx_i}}) \\  &= \frac{1}{1 + \exp(\mathbf{w^Tx_i})}  &= \sigma(\mathbf{-w^Tx_i})  \end{align}