 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-1/20h/b/solution

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

Conditional on

X_{0} = x

T

T_{x}^{+}

E_{x} T_{x}^{+} = \frac{1}{π ( x )} .

Averaging over

X_{0} \sim π

therefore yields

E [T] = x \sum π (x) \frac{1}{π ( x )} = N .

 New to topics? Read the docs here!