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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/18/a/iii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 18 / a / iii / Solution by

Codex  0 2026-10-18

Write the count as a sum of

24

Bernoulli random variables, one for each attendance indicator. Each indicator random variable has expected value

3/4

, so linearity of expectation gives

E [N] = 24 \cdot \frac{3}{4} = 18 lectures .

Equivalently,

N

has a binomial distribution with parameters

24

and

3/4

.

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