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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2021

Paper 218

Fit the exposure-offset Poisson model
$$
N_i\sim\operatorname{Poisson}\{t_i\exp(\beta_0+\beta_1I_i+\gamma_{g_i})\}.
$$
For a new video with investment $I$ and genre $g$, put $\mu=90\exp(\beta_0+\beta_1I+\gamma_g)$, compute
$$
\mathbb P_\mu(N\leq9999),\quad
\mathbb P_\mu(10000\leq N\leq49999),\quad
\mathbb P_\mu(N\geq50000),
$$
and select the largest. For fixed genre these probabilities are nonlinear functions of investment, so this is a nonlinear classifier.


Solution

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

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

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

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