% Cases f(x) = \begincases 0 & x<0 \ 1 & x\ge 0 \endcases Create rayanne_macros.sty :
\subsectionPart (b): First-order conditions Taking the derivative w.r.t. $\mu$: TsLatex Rayanne Lenox
\subsectionPart (a): Derive the log-likelihood Given $y_i \sim \mathcalN(\mu, \sigma^2)$ i.i.d., the log-likelihood is: % Cases f(x) = \begincases 0 & x<0
\beginalign \ell(\mu, \sigma^2) &= \sum_i=1^n \log f(y_i \mid \mu, \sigma^2) \ &= -\fracn2\log(2\pi) - \fracn2\log\sigma^2 - \frac12\sigma^2\sum_i=1^n (y_i - \mu)^2 \labeleq:loglik \endalign the log-likelihood is: \beginalign \ell(\mu
% Text in math \textsubject to % inside \text{}
% Matrices \beginpmatrix a & b \ c & d \endpmatrix
Then in your main file: