 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/m/m4/a/ii/solution

Replacement and mixing make the one hundred draws independent and identically distributed. Writing

S = \sum_{j = 1}^{100} X_{j}

E S = 100 \cdot 4 = 400, Var (S) = 100 \cdot \frac{28}{5} = 560.

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