 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-35/4/b/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

The intercept is the midpoint of the two log odds:

α = \frac{1}{2} [logit θ_{C} + logit θ_{T}] .

Equivalently

e^{α}

is the geometric mean of the two odds. The logistic function evaluated at

α

represents a central event probability, and approximates the average of the two group probabilities when

β

is small. It is not generally their arithmetic average, nor is

α

specifically the control-group log odds.

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