 Solution

ID: past-exam-of-the-probability-course-of-the-university-of-oxford/2021/1/c/i/solution

T_{0} = 0

and

E_{j} = T_{j} - T_{j - 1}

E_{j}

E E_{j} = 1

and

Var (E_{j}) = 1

, so the finite, positive variance hypothesis of the central limit theorem holds. Since

T_{n} = \sum_{j = 1}^{n} E_{j}

\frac{T _{n} - n}{n} = \frac{1}{n} j = 1 \sum n (E_{j} - 1) d N (0, 1) .

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