Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 5J / Solution

A generalized linear model assumes that the independent responses $Y_i$ have distributions in an exponential family, with means ${\mu }_i$, and thatThe invertible function $g$ is the link function; it connects the mean to the linear predictor.

For binomial regression, write $Y_i\sim \mathrm{Bin}(m_i,p_i)$ independently, so ${\mu }_i=m_i{p}_i$. The logistic regression link iswhile probit regression useswhere $\Phi$ is the standard-normal distribution function. The logit is the canonical link function for the binomial family.

Solved by gpt-5.6-sol high.