Alternative Equation Formats

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MathML

\begin{array}{rcl} V_{k k} & = & \sum_{j = 1}^{D} {\frac{d_{j} (Y_{j} - d_{j})}{Y_{j} (Y_{j} - 1)} \sum_{i = 1}^{Y_{j}} [{(\frac{Y_{j k}^{w}}{Y_{j}^{w}})}^{2} w_{i}^{2} I {X_{i} \neq k} + {(\frac{Y_{j}^{w} - Y_{j k}^{w}}{Y_{j}^{w}})}^{2} w_{i}^{2} I {X_{i} = k}]}, 1 \leq k \leq K \\ V_{k h} & = & \sum_{j = 1}^{D} {\frac{d_{j} (Y_{j} - d_{j})}{Y_{j} (Y_{j} - 1)} \sum_{i = 1}^{Y_{j}} [\frac{Y_{j k}^{w} Y_{j h}^{w}}{(Y_{j}^{w})^{2}} w_{i}^{2} I {X_{i} \neq k, h} - \frac{(Y_{j}^{w} - Y_{j k}^{w}) Y_{j h}^{w}}{(Y_{j}^{w})^{2}} w_{i}^{2} I {X_{i} = k} \\ - \frac{(Y_{j}^{w} - Y_{j h}^{w}) Y_{j k}^{w}}{(Y_{j}^{w})^{2}} w_{i}^{2} I {X_{i} = h}]}, 1 \leq k \neq h \leq K \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} {V}_{kk} & = & \sum _{j=1}^ D \left\{ \frac{d_ j(Y_ j-d_ j)}{Y_ j(Y_ j-1)} \sum _{i=1}^{Y_ j} \left[ \left( \frac{Y^ w_{jk}}{Y^ w_ j }\right)^2 w^2_ iI\{ X_ i\neq k\} + \left( \frac{Y^ w_ j - Y^ w_{jk}}{Y^ w_ j }\right)^2 w^2_ i I\{ X_ i=k\} \right] \right\} , \quad 1\leq k \leq K \\ {V}_{kh} & = & \sum _{j=1}^ D \left\{ \frac{d_ j(Y_ j-d_ j)}{Y_ j(Y_ j-1)} \sum _{i=1}^{Y_ j} \left[ \frac{Y^ w_{jk} Y^ w_{jh}}{(Y^ w_ j)^2} w^2_ iI\{ X_ i\neq k, h\} - \frac{(Y^ w_ j - Y^ w_{jk})Y^ w_{jh}}{(Y^ w_ j)^2} w^2_ i I\{ X_ i=k\} \right. \right. \\ & & \left. \left. - \frac{(Y^ w_ j - Y^ w_{jh})Y^ w_{jk}}{(Y^ w_ j)^2} w^2_ i I\{ X_ i=h\} \right] \right\} , \quad 1 \leq k \neq h \leq K \end{eqnarray*}