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: <math>
\ln \Pr(Y_i=k) = \boldsymbol\beta_k \cdot \mathbf{X}_i - \ln Z \;\;\;\;,\;\;k \le K.
</math>
As in the binary case, we need an extra term <math>- \ln Z</math> to ensure that the whole set of probabilities forms a [[probability distribution]], i.e. so that they all sum to one:
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