The graph of the associated probability density function is "bell"-shaped, and is known as the Gaussian function or bell curve:[nb 1]
Above is a picture of the famous bell curve. The formula is there to show that there is a formula, that the curve is a graph of points above the base line.
You might not have known the formula, or even that the formula existed, but you know the general idea that the bigger the error, the less likely it is to occur. So, it is more likely that I will mistype a single lettor than a whole drow. But, of course, "more likely" is not the same thing as "impossible", now is it? You know that old image of a thousand monkeys typing away at keyboards. The idea is that if they bang on the keys enough, they might stumble on typing out the exact text of "Hamlet". It is just a mental image and we don't have the monkeys, the keyboards, or enough time to really see if they could.
The normal curve is a common model of errors or any random variable. Some random variables are not well-modeled by the normal curve so statisticians actually have a large tool box of models that they may employ to model errors and forecast. For instance, I have always thought that it is a mistake not to introduce people to the Poisson model, which is actually easier to use than the normal curve and applies to many errors and random events which often don't happen, such as getting a flat tire.
The world, nature and everything in the world are tricky and don't seem to behave in a way that is easy for people to understand, forecast, or control.
I am going to be without my usual copy editor for a while. That means a good chance of increased typos in these blog posts until she is back on the job. I try to look at what I have typed as completely as I can but I often do not notice a misspelled word or some other sort of error. More often than I want, the error changes the meaning of what I want to write, such as leaving an important "not" out of a sentence. Making a positive sentence out of something I mean to be negative happens more often than I like. I don't like if it ever happens but it does in say, one in 10 or 15 of my messages.
--
Bill
Main blog: Fear, Fun and Filoz
Main web site: Kirbyvariety
