Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Discrete mathematics, continuous mathematics, and probability / 8 / b / i / Solution

Using the rate parameter convention for the exponential distribution, independence gives the joint probability density functionFor $z\ge 0$, the survival probability of the minimum isThus $Z$ has exponential distribution with rate $3$, andValues of a probability density function at the single endpoint $0$ do not affect the probability distribution.