Check that if (p_{j}left(mathbf{x}_{i} ight)) is small, then (frac{p_{j}left(mathbf{x}_{i} ight)}{1-p_{j}left(mathbf{x}_{i} ight)} approx p_{j}left(mathbf{x}_{i} ight)) and hence (8.17)

Check that if \(p_{j}\left(\mathbf{x}_{i}\right)\) is small, then \(\frac{p_{j}\left(\mathbf{x}_{i}\right)}{1-p_{j}\left(\mathbf{x}_{i}\right)} \approx p_{j}\left(\mathbf{x}_{i}\right)\) and hence (8.17) implies \(p_{j}\left(\mathbf{x}_{i}\right) \approx\) \(\phi\left(\mathbf{x}_{i} ; \boldsymbol{\beta}\right) p_{j}(\mathbf{0})\).