 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/d/solution

P_{2} (t) = ⎩ ⎨ ⎧ 0, t^{2} / T_{2}^{2}, 1, t \leq 0, 0 < t < T_{2}, t \geq T_{2} .

Its graph is an upward-curving parabolic arc from

(0, 0)

(T_{2}, 1)

, followed by a horizontal plateau. Both cumulative functions are continuous at their upper support endpoints.

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