= Solution
A <generalized linear model> specifies independent responses in an <exponential dispersion family>, their means $\mu_i=E(Y_i)$, and a <link function> connecting those means to a <linear predictor>. In the common notation,
$$
f_i(y_i)=\exp\left\{\frac{y_i\theta_i-b(\theta_i)}{a_i\phi}+c_i(y_i,a_i\phi)\right\},
\qquad\mu_i=b'(\theta_i),\quad\operatorname{Var}(Y_i)=a_i\phi V(\mu_i),
$$
where $a_i$ are known positive weights, $\phi$ is the common <dispersion parameter>, and $V(\mu_i)=b''(\theta_i)$ is the <variance function>. The systematic part is
$$
\boxed{g(\mu_i)=x_i^T\beta.}
$$
Here $x_i$ is a row of the known <design matrix> and $\beta$ contains the unknown regression coefficients. The <link function> is invertible on the permitted mean domain; the <canonical link function> takes the mean to the natural parameter. This separates distributional, predictor, and link assumptions: it does not require the response itself to be normally distributed or the mean itself to be linear in the covariates.
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