Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 5K / Solution

Logistic regression assumes independent $Y_i\mid X_i\sim \mathrm{Bernoulli}({\pi }_i)$ withFor the binomial exponential family, $\ell =y\theta -m\log (1+e^{\theta })+\text{constant}$, so the mean is $m{e}^{\theta }/(1+e^{\theta })$ and the canonical parameter is its logit. It may be fitted by iteratively reweighted least squares.

Under LDA, Bayes' rule giveswhich is a logistic model with an intercept.