 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/b/i/solution

Since

Y \geq 1

, its finite expected value satisfies

1 \leq μ < \infty

. Every

q_{k} = k p_{k} / μ

is nonnegative and

\sum_{k \geq 1} q_{k} = \frac{1}{μ} \sum_{k \geq 1} k p_{k} = \frac{E Y}{μ} = 1.

Y

: larger values receive proportionally more weight.

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