Alternative Equation Formats

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MathML

V a r [ Z c s ( X ) ] 4 k 2 N p ( 1 p ) + k 2 [ 1 P ( X = N p 0 ) ] k 2 [ P ( X < N p 0 ) P ( X > N p 0 ) ] 2 + 4 k 2 [ E ( X 1 { X < N p 0 } ) E ( X 1 { X > N p 0 } ) ] 4 k 2 N p [ P ( X < N p 0 ) P ( X > N p 0 ) ]

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Math as LaTeX Source

\begin{align*} \mr{Var} \left[Z_{cs}(X)\right] & \approx 4 k^2 N p (1-p) + k^2 \left[ 1 - P(X = N p_0) \right] - k^2 \left[ P(X<Np_0) - P(X>Np_0) \right]^2 \\ & \quad + 4 k^2 \left[ E\left(X 1_{\{ X<Np_0\} }\right) - E\left(X 1_{\{ X>Np_0\} }\right) \right] - 4 k^2 N p \left[P(X<Np_0) - P(X>Np_0)\right] \\ \end{align*}