 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-3/20h/b/solution

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

Combining the independent standard normal variable

n (\overline{X} - μ) / σ

with the independent chi-squared variable

S_{XX} / σ^{2}

gives

\frac{n ( X - μ )}{S _{XX} / ( n - 1 )} \sim t_{n - 1},

n - 1

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