Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 2 / 11F / c

Table of contents
- Solution c

Solution

For the process to stop on toss

n

, the last toss must be the

k

th head, while the first

n - 1

tosses must contain exactly

k - 1

heads. Hence the negative binomial distribution gives

P (T = n) = (k - 1 n - 1) p^{k} (1 - p)^{n - k}, n \geq k .

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