Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 5J / b

For independent observations from an exponential dispersion family with common known dispersion parameter ${\sigma }^2$, the generalized linear model log-likelihood iswhere ${\mu }_i=b^{\prime }({\theta }_i)$ and the link function satisfies $g({\mu }_i)={\eta }_i=x_i^T\beta$.