 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/ia/paper-2/11f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

[0, 1]

and zero elsewhere,

f_{X + Y} (u) = \int_{R} 1_{[0, 1]} (x) 1_{[0, 1]} (u - x) d x .

This is the length of

[0, 1] \cap [u - 1, u]

. Therefore the density is

f_{X + Y} (u) = ⎩ ⎨ ⎧ u 2 - u 0 0 \leq u \leq 1, 1 \leq u \leq 2, otherwise .

 New to topics? Read the docs here!