Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics, and probability / Probability / 7 / a / ii

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- Solution ii

Solution

For finite second moments, the variance of a sum is

var (i = 1 \sum n X_{i}) = i = 1 \sum n var (X_{i}) + 2 1 \leq i < j \leq n \sum cov (X_{i}, X_{j}) = i, j = 1 \sum n cov (X_{i}, X_{j}) .

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