 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-1/19h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

The power function of a test is the probability of rejection as a function of the true parameter. Since

S = n \overline{X} \sim Γ (n, λ)

β (λ) = P_{λ} (\overline{X} > c_{α}) = 1 - G_{n, λ} (n c_{α}) .

At the null value,

β (λ_{0}) = α

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