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MathML

\begin{aligned} V a r [Z_{c s L} (X)] & \approx 4 k^{2} N p (1 - p) + k^{2} [1 - P (X = N θ_{L})] - k^{2} {[P (X < N θ_{L}) - P (X > N θ_{L})]}^{2} \\ + 4 k^{2} [E (X 1_{{X < N θ_{L}}}) - E (X 1_{{X > N θ_{L}}})] - 4 k^{2} N p [P (X < N θ_{L}) - P (X > N θ_{L})] \\ V a r [Z_{c s U} (X)] & \approx 4 k^{2} N p (1 - p) + k^{2} [1 - P (X = N θ_{U})] - k^{2} {[P (X < N θ_{U}) - P (X > N θ_{U})]}^{2} \\ + 4 k^{2} [E (X 1_{{X < N θ_{U}}}) - E (X 1_{{X > N θ_{U}}})] - 4 k^{2} N p [P (X < N θ_{U}) - P (X > N θ_{U})] \end{aligned}

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Math as LaTeX Source

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