 Solution

ID: past-exam-of-the-martingales-and-financial-mathematics-course-of-the-university-of-oxford/2008/a/2/b/i/solution

The variables are independent and identically distributed if they all have one common probability distribution and every finite selection satisfies

P (X_{n_{1}} \in B_{1}, \dots, X_{n_{k}} \in B_{k}) = \prod_{j = 1}^{k} P (X_{n_{j}} \in B_{j})

for distinct indices and arbitrary Borel sets. The condition concerns joint distributions, not merely pairwise correlations.

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