I was trying to emulate a random currency value, and first thing I thought was to start with value 1 and then iteratively add, say,
Rand(-.1, .1), which is a function call that gives me a random number between
.1. I then realized this could take my currency's value to less than zero, which would make no sense.
So I figured every new value should be proportional to the old value, and tested multiplying the value times
Rand(0, 2) iteratively. My intuition behind it was that since is as likely for
Rand(0, 2) to give a number < 1 than a number > 1, the value is as likely to increase as is to decrease. But then for every test I ran the value dropped quickly to almost zero. So I gave
Rand(0, e) (
e is the constant 2.718...) a try and it seemed to magically work (I also tried with
Rand(0, 3) and it grew way above 1 every time).
This was really just a wild guess, and my question is, was my guess right or is this just a coincidence, and if it was, why does it work?