 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2011/o/3/b/solution

Let

t_{ν, β}

denote a quantile of the Student t-distribution with

ν = n - 1

P (∣ Y ∣ \leq t_{n - 1, 1 - α /2}) = 1 - α

. Solving for

μ

gives the exact central confidence interval

[\overline{X} - t_{n - 1, 1 - α /2} \frac{S}{n}, \overline{X} + t_{n - 1, 1 - α /2} \frac{S}{n}] .

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