Compound Interest and the Exponential Distribution | by Rohit Pandey …

Your mortgage is memory-less and so is the exponential distribution

There are many interesting events that happen at points in time. For example, the arriavals of busses at a bus stop, accidents on a highway, goals scored in a soccer (football) game. The processes that model such point in time events are called “point processes”. An important consideration in these processes is how long it takes from one event to the next. For example, given you just missed a bus, how long will you have to wait for the next bus? This time is a random variable and the choice of the random variable specifies the point process. One choice for this random variable is something that isn’t very random (deterministic numbers are just a special case of random ones). Busses arriving on a punctual schedule, every 10 minutes for example. This might sound like the simplest possible point process, but there is something even simpler. And it arises…