 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability/7/c/i/solution

E [X_{i}] = \frac{- 1 + 0 + 1}{3} = 0, E [X_{i}^{2}] = \frac{1 + 0 + 1}{3} = \frac{2}{3}, var (X_{i}) = \frac{2}{3} .

Let

S_{m} = \sum_{i = 1}^{m} X_{i}

E [S_{m}] = 0, var (S_{m}) = \frac{2 m}{3} .

The independence is needed for the variance calculation, but not for the mean.

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