 Solution

ID: past-exam-of-the-mathematical-and-computational-biology-course-of-the-university-of-cambridge/2025/paper-1/6/a/solution

For independent geometric random variables supported on

1, 2, \dots

, put

S = \sum_{i} x_{i}

L (p) = p^{n} (1 - p)^{S - n}, 0 < p < 1.

There are

n

terminal successes and

S - n

preceding failures.

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