Possibly unhelpful answer: Arguably none! This is presented as a surprising fact, but you could easily argue that this is the proper definition of an exponential distribution. If you do
x = -log(rand())/lambda
a bunch a times, that comes from something, right? Well, let's call that something an exponential distribution.
From this perspective, the thing that actually needs math is finding the density function of the exponential distribution. (For that, in theory you just need calc 101 and probability 101.)
x = -log(rand())/lambda
a bunch a times, that comes from something, right? Well, let's call that something an exponential distribution.
From this perspective, the thing that actually needs math is finding the density function of the exponential distribution. (For that, in theory you just need calc 101 and probability 101.)