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

Write the chocolate count as $K_n={\sum }_{j=1}^n{I}_j$ with independent Bernoulli random variables. Each has expected value $p$ and variance $p(1-p)$. By linearity of expected value and additivity of variance for independent variables,