Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 101 / 1 / b / Solution

For $t\ge 0$, independence factors the survival function of the minimum:The minimum is nonnegative, and this is exactly the survival function of an exponential distribution. HenceThe parameter here is the rate, rather than the mean. The calculation is the simplest example of competing exponential clocks.