Alternative Equation Formats

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MathML

\begin{aligned} P (X = N θ_{L}) & = 0 \\ P (X = N θ_{U}) & = 0 \\ P (X < N θ_{L}) & = Φ (d_{L}) \\ P (X < N θ_{U}) & = Φ (d_{U}) \\ P (X > N θ_{L}) & = 1 - Φ (d_{L}) \\ P (X > N θ_{U}) & = 1 - Φ (d_{U}) \\ E (X 1_{{X < N θ_{L}}}) & = N p Φ (d_{L}) - {[N p (1 - p)]}^{\frac{1}{2}} ϕ (d_{L}) \\ E (X 1_{{X < N θ_{U}}}) & = N p Φ (d_{U}) - {[N p (1 - p)]}^{\frac{1}{2}} ϕ (d_{U}) \\ E (X 1_{{X > N θ_{L}}}) & = N p [1 - Φ (d_{L})] + {[N p (1 - p)]}^{\frac{1}{2}} ϕ (d_{L}) \\ E (X 1_{{X > N θ_{U}}}) & = N p [1 - Φ (d_{U})] + {[N p (1 - p)]}^{\frac{1}{2}} ϕ (d_{U}) \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} P(X=N\theta _ L) & = 0 \\ P(X=N\theta _ U) & = 0 \\ P(X<N\theta _ L) & = \Phi (d_ L) \\ P(X<N\theta _ U) & = \Phi (d_ U) \\ P(X>N\theta _ L) & = 1 - \Phi (d_ L) \\ P(X>N\theta _ U) & = 1 - \Phi (d_ U) \\ E\left(X 1_{\{ X<N\theta _ L\} }\right) & = Np\Phi (d_ L) - \left[ N p (1-p) \right]^\frac {1}{2} \phi (d_ L) \\ E\left(X 1_{\{ X<N\theta _ U\} }\right) & = Np\Phi (d_ U) - \left[ N p (1-p) \right]^\frac {1}{2} \phi (d_ U) \\ E\left(X 1_{\{ X>N\theta _ L\} }\right) & = Np\left[ 1 - \Phi (d_ L) \right] + \left[ N p (1-p) \right]^\frac {1}{2} \phi (d_ L) \\ E\left(X 1_{\{ X>N\theta _ U\} }\right) & = Np\left[ 1 - \Phi (d_ U) \right] + \left[ N p (1-p) \right]^\frac {1}{2} \phi (d_ U) \\ \end{align*}