 Solution

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

X_{n}

are independent and identically distributed real random variables with

E ∣ X_{1} ∣ < \infty

, then

\frac{1}{N} n = 1 \sum N X_{n} ⟶ E X_{1} almost surely .

The first absolute moment condition is part of the standard statement.

 New to topics? Read the docs here!