 Solution

ID: 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/solution

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.

 New to topics? Read the docs here!