Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 218 / 3 / a / Solution

Time is exposure: doubling the public duration should double the expected count without changing the viewing rate. Modeling the rate is therefore preferable to treating time as an additive linear predictor. In a Poisson regression the exact implementation should beusing $\log t_i$ as an offset; directly supplying noninteger $N_i/t_i$ without exposure weights is not generally likelihood-equivalent.