Tslatex Rayanne Lenox May 2026

\beginproof This follows from solving $\frac\partial \ell\partial \sigma^2=0$ using \eqrefeq:loglik. \endproof

\beginalign \frac\partial \ell\partial \mu = \frac1\sigma^2\sum_i=1^n (y_i - \mu) \stackrelset= 0 \ \implies \hat\mu_MLE = \bary \endalign TsLatex Rayanne Lenox

\subsectionPart (a) \beginalign y = \beta_0 + \beta_1 x + \varepsilon \endalign TsLatex Rayanne Lenox

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\subsectionPart (b): First-order conditions Taking the derivative w.r.t. $\mu$: TsLatex Rayanne Lenox