Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / 12 / a

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- Solution a

Solution

Write

\overset{s}{ˉ} > 0

for the mean in minutes. An exponential distribution with that mean has rate

1/ \overset{s}{ˉ}

, so its probability density function is

f_{S} (s) = {\overset{s}{ˉ}^{- 1} e^{- s / \overset{s}{ˉ}}, 0, s \geq 0, s < 0.

The density has units of inverse minutes, ensuring that its integral is a dimensionless probability.

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