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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2003/iii/paper-79/1/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 79 / 1 / a / Solution by

Codex  0 Created 2026-10-03 Updated 2026-10-14

At large-deviation speed

L

, the exponential distribution gives the large deviation principle on

R

with good rate function

J (b) = {λb, + \infty, b \geq 0, b < 0.

In particular,

P (B / L \geq b) = e^{- λ L b}

for

b \geq 0

. Its finite sublevel sets are the compact sets

[0, r / λ]

.

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