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

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- Solution d

Solution

Fit the exposure-offset Poisson model

N_{i} \sim Poisson {t_{i} exp (β_{0} + β_{1} I_{i} + γ_{g_{i}})} .

For a new video with investment

I

and genre

g

, put

μ = 90 exp (β_{0} + β_{1} I + γ_{g})

, compute

P_{μ} (N \leq 9999), P_{μ} (10000 \leq N \leq 49999), P_{μ} (N \geq 50000),

and select the largest. For fixed genre these probabilities are nonlinear functions of investment, so this is a nonlinear classifier.

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