Alternative Equation Formats

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MathML

\begin{aligned} E [Y] & = μ_{i} + \sqrt{ϕ} \frac{p h i (\frac{a - μ_{i}}{\sqrt{ϕ}}) - p h i (\frac{b - μ_{i}}{\sqrt{ϕ}})}{Φ (\frac{b - μ_{i}}{\sqrt{ϕ}}) - Φ (\frac{a - μ_{i}}{\sqrt{ϕ}})} \\ V a r [Y] & = ϕ [1 + \frac{\frac{a - μ_{i}}{\sqrt{ϕ}} p h i (\frac{a - μ_{i}}{\sqrt{ϕ}}) - \frac{b - μ_{i}}{\sqrt{ϕ}} p h i (\frac{b - μ_{i}}{\sqrt{ϕ}})}{Φ (\frac{b - μ_{i}}{\sqrt{ϕ}}) - Φ (\frac{a - μ_{i}}{\sqrt{ϕ}})} \\ - {\frac{p h i (\frac{a - μ_{i}}{\sqrt{ϕ}}) - p h i (\frac{b - μ_{i}}{\sqrt{ϕ}})}{Φ (\frac{b - μ_{i}}{\sqrt{ϕ}}) - Φ (\frac{a - μ_{i}}{\sqrt{ϕ}})}}^{2}] \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} \mr{E}[Y] & = \mu _ i + \sqrt{\phi } \frac{\mr{phi}\left(\frac{a-\mu _ i}{\sqrt{\phi }} \right) - \mr{phi}\left(\frac{b-\mu _ i}{\sqrt{\phi }} \right)}{\Phi \left(\frac{b-\mu _ i}{\sqrt{\phi }} \right) - \Phi \left(\frac{a-\mu _ i}{\sqrt{\phi }} \right)}\\ \mr{Var}[Y] & = \phi \left[1 + \frac{\frac{a-\mu _ i}{\sqrt{\phi }} \mr{phi}\left(\frac{a-\mu _ i}{\sqrt{\phi }} \right) - \frac{b-\mu _ i}{\sqrt{\phi }} \mr{phi}\left(\frac{b-\mu _ i}{\sqrt{\phi }} \right)}{\Phi \left(\frac{b-\mu _ i}{\sqrt{\phi }} \right) - \Phi \left(\frac{a-\mu _ i}{\sqrt{\phi }} \right)} \right. \\ & - \left. \left\{ \frac{\mr{phi}\left(\frac{a-\mu _ i}{\sqrt{\phi }} \right) - \mr{phi}\left(\frac{b-\mu _ i}{\sqrt{\phi }} \right)}{\Phi \left(\frac{b-\mu _ i}{\sqrt{\phi }} \right) - \Phi \left(\frac{a-\mu _ i}{\sqrt{\phi }} \right)}\right\} ^2 \right] \end{align*}