Alternative Equation Formats

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MathML

\begin{aligned} l_{1} (p; y) & = {\begin{cases} y \log {p} & y > 0 \\ 0 & o t h e r w i s e \end{cases} \\ l_{2} (p; y) & = {\begin{cases} (1 - y) \log {1 - p} & y < 1 \\ 0 & o t h e r w i s e \end{cases} \\ l (p; y) & = l_{1} (p; y) + l_{2} (p; y) \\ E [Y] & = p \\ V a r [Y] & = p (1 - p) \\ 0 & < p < 1 \end{aligned}

Math Rendered as SVG

Math as LaTeX Source

\begin{align*} l_1(p;y) & = \left\{ \begin{array}{ll} y \, \, \log \{ p\} & y > 0 \cr 0 \phantom{(1-y)\, \, \log \{ 1-p\} } & \mr{otherwise} \end{array} \right. \\ l_2(p;y) & = \left\{ \begin{array}{ll} (1-y)\, \, \log \{ 1-p\} \phantom{0} & y < 1 \cr 0 & \mr{otherwise} \end{array} \right. \\ l(p;y) & = l_1(p;y) + l_2(p;y) \\ \mr{E}[Y] & = p \\ \mr{Var}[Y] & = p\, (1-p) \\ 0 & < p < 1 \end{align*}