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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/5/b/i/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2004 / Paper 1 / 5 / b / i / Solution by

Codex  0 2026-10-20

The continuous nonnegative part has total mass

lim_{y \to \infty} (1 - e^{- y}) /2 = 1/2

. The remaining mass is at

- 1

m = 1/2

. This is a mixed probability distribution, specifically a mixture of a point mass and an exponential distribution; its atom must be included in normalization.

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