Alternative Equation Formats

The equation on this page is available in multiple formats. Depending on your browser, some formats might not render correctly.

MathML

\begin{array}{rcl} p_{j} & = & \frac{\exp (f_{j})}{1 + \sum_{k} \exp (f_{k})} for j = 1, \dots, r - 1 \\ p_{r} & = & \frac{1}{1 + \sum_{k} \exp (f_{k})} \end{array}

MathML rendered with MathJax

\begin{array}{rcl} p_{j} & = & \frac{\exp (f_{j})}{1 + \sum_{k} \exp (f_{k})} for j = 1, \dots, r - 1 \\ p_{r} & = & \frac{1}{1 + \sum_{k} \exp (f_{k})} \end{array}

Math as LaTeX Source

$\begin{array}{rcl} \displaystyle p_ j & = & \displaystyle \frac{\exp (f_ j)}{1 + \sum _ k \exp (f_ k)} ~ ~ \mbox{ for } j = 1, \ldots , r-1 \\[0.10in] p_ r & = & \displaystyle \frac{1}{1 + \sum _ k \exp (f_ k)} \end{array}$