Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Discrete mathematics, continuous mathematics and probability / 7 / a / i

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- Solution i

Solution

The variable has positive-integer support, so

P (X > 0) = 1

. Subtract consecutive values of the survival function:

P (X = k) = P (X > k - 1) - P (X > k) = p (1 - p)^{k - 1}, k \geq 1.

This is the positive-support convention for the geometric distribution.

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