 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/14/b/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 2 / 14 / b / Solution by

Codex  0 2026-10-18

Normalization requires

1 = \int_{0}^{T_{2}} A t d t = A T_{2}^{2} /2

. Therefore

A = \frac{2}{T _{2}^{2}}, f_{2} (t) = {2 t / T_{2}^{2}, 0, 0 < t < T_{2}, otherwise .

(1)

The graph rises linearly from zero to the left-hand limit

2/ T_{2}

, then drops to zero beyond

T_{2}

. Its enclosed triangular area is one. The combined sketch in (f) uses dimensionless time and shows this density together with the cumulative probabilities.

 Read the full article

 New to topics? Read the docs here!