Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2003 / Paper 2 / 5 / b / ii

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- Solution ii

Solution

The survival function of this exponential distribution is

P (X \geq t) = e^{- k t}

for

t \geq 0

. Since

{X \geq 3} \subseteq {X \geq 1}

, the conditional probability is

P (X \geq 3 ∣ X \geq 1) = \frac{e ^{- 3 k}}{e ^{- k}} = e^{- 2 k} .

This is the memoryless property: after surviving the first unit, surviving two additional units has the same probability as it did initially.

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