 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/12/a/ii/solution

Write the chocolate count as

K_{n} = \sum_{j = 1}^{n} I_{j}

p

p (1 - p)

. By linearity of expected value and additivity of variance for independent variables,

\overline{k}_{n} = n p, V_{n} = n p (1 - p) .

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