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MathML

\begin{aligned} Z (X) & = \frac{n_{01} - n_{D} (0.5)}{{[n_{D} 0.5 (1 - 0.5)]}^{\frac{1}{2}}} \overset{\cdot}{\sim} N (\frac{n_{D}^{\frac{1}{2}} (\frac{π_{01}}{π_{01} + π_{10}} - 0.5)}{{[0.5 (1 - 0.5)]}^{\frac{1}{2}}}, \frac{\frac{π_{01}}{π_{01} + π_{10}} (1 - \frac{π_{01}}{π_{01} + π_{10}})}{0.5 (1 - 0.5)}) \\ = \frac{n_{01} - (n_{01} + n_{10}) (0.5)}{{[(n_{01} + n_{10}) 0.5 (1 - 0.5)]}^{\frac{1}{2}}} \\ = \frac{n_{01} - n_{10}}{{[n_{01} + n_{10}]}^{\frac{1}{2}}} \\ = \sqrt{Q_{M_{0}}} \end{aligned}

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Math as LaTeX Source

\begin{align*} Z(X) & = \frac{n_{01} - n_ D (0.5)}{\left[ n_ D 0.5(1-0.5) \right]^\frac {1}{2}} \quad {\stackrel{\cdot }{\thicksim }} \; \mr{N}\left(\frac{n_ D^{\frac{1}{2}}(\frac{\pi _{01}}{\pi _{01}+\pi _{10}} - 0.5)}{\left[ 0.5(1-0.5) \right]^\frac {1}{2}}, \frac{\frac{\pi _{01}}{\pi _{01}+\pi _{10}} \left(1-\frac{\pi _{01}}{\pi _{01}+\pi _{10}}\right)}{0.5(1-0.5)}\right) \\ & = \frac{n_{01} - (n_{01} + n_{10}) (0.5)}{\left[ (n_{01} + n_{10}) 0.5(1-0.5) \right]^\frac {1}{2}} \\ & = \frac{n_{01} - n_{10}}{\left[ n_{01} + n_{10} \right]^\frac {1}{2}} \\ & = \sqrt{Q_{M_0}} \\ \end{align*}