Alternative Equation Formats

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MathML

\begin{array}{rcl} \hat{V} (\hat{β}) & = & \sum_{r = 1}^{R_{a}} α_{r} ({\hat{β}}_{r} - \hat{β}) {({\hat{β}}_{r} - \hat{β})}^{'} + (R - R_{a}) {\frac{1}{R_{a}} \sum_{r = 1}^{R_{a}} α_{r} ({\hat{β}}_{r} - \hat{β}) {({\hat{β}}_{r} - \hat{β})}^{'}} \\ = & \frac{R}{R_{a}} \sum_{r = 1}^{R_{a}} α_{r} ({\hat{β}}_{r} - \hat{β}) ({\hat{β}}_{r} - \hat{β})^{'} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \widehat{\mb{V}}(\hat{\bbeta }) & = & \sum _{r=1}^{R_ a} \alpha _ r \left( {\hat{\bbeta }_ r} - \hat{\bbeta } \right) \left( {\hat{\bbeta }_ r} - \hat{\bbeta } \right)' + (R-R_ a) \left\{ \frac{1}{R_ a} \sum _{r=1}^{R_ a} \alpha _ r \left( {\hat{\bbeta }_ r} - \hat{\bbeta } \right) \left( {\hat{\bbeta }_ r} - \hat{\bbeta } \right)' \right\} \\ & = & \frac{R}{R_ a} \sum _{r=1}^{R_ a} \alpha _ r(\hat{\bbeta }_ r - \hat{\bbeta }) (\hat{\bbeta }_ r - \hat{\bbeta })' \end{eqnarray*}