Roll a (fair) die, and a number from 1 to 6 shows up. Roll it again, and a different number comes up. Or maybe the same number comes up. The result of the first roll of the die has nothing to do with the result of the second. Roll the same die a thousand times, and you would expect each number to show up roughly 166 times, or one-sixth of the time.
Each roll is an event that results in a random result. There’s no relationship between one result and the next. The result of one roll is independent of the result of the previous roll, and neither roll has anything to do with the next.
In days of old when men were bold and the Internet hadn’t been invented, the phone company printed a telephone directory and delivered it to your house. (They still do, in fact, and no matter how much I plead, complain, or threaten, they still deliver one to my house every year. It goes right into the recycling bin.) If you open to any page and read down the column of phone numbers, you have a fairly good approximation of random numbers.
I know: Yeah, so what?
We can use random numbers to generate a set of results that look like die rolls, or coin tosses, or arrivals in a queue, or daily usages of a part, or whatever we want it to be. Let’s do coin tosses as an example. I’m going to use a site called Random.org and generate a list of ten two-digit random numbers from 00 to 99. If the number is even, the result was “heads,” and if odd, “tails.”
which we interpret as tails, tails, heads, tails, heads, heads, heads, heads, heads, and tails.
Generating random numbers and using them to simulate events is a big part of using stochastic processes (simulation of the evolution of some variable over time). For example, I read recently that in the US a man between 18 and 44 will change jobs an average of 11.4 times, with a quarter changing 15 times or more and twelve percent changed jobs 4 times or fewer. Based on those numbers, I ran a stochastic process to see what the average career looks like.
I know, I’m strange.
By the way, when I decide to visit others in the A to Z Challenge, I generate a dozen random numbers between 1 and 2107, the number of blogs on the list. Works for me!