Solution
= Solution
For independent observations from an <exponential dispersion family> with common known <dispersion parameter> $\sigma^2$, the <generalized linear model> log-likelihood is
$$
\boxed{
\ell(\beta)
=\sum_{i=1}^n
\left[
\frac{y_i\theta_i-b(\theta_i)}{\sigma^2}
+c(y_i,\sigma^2)
\right],
}
$$
where $\mu_i=b'(\theta_i)$ and the <link function> satisfies $g(\mu_i)=\eta_i=x_i^T\beta$.