What exactly is the difference between the mean waiting time and the median waiting time for an exponential distribution? I'm looking for a slightly intuitive understanding. I know the formulae, with the mean waiting time as 1/λ and the median as ln2/λ (which I notice is also the formula for half-life in radioactive decay), but I'm still trying to grasp the essence of what these values actually mean. Does anyone have some useful analogies? I don't like solving these problems by plugging in values without a proper understanding of the method.