Re:Do the math: too much calculus? (2012)
by rocqua on Thursday October 20, 2016 @04:14AM
(#12750526)
The chance of choosing 0.5 from the interval 0 to 1 is 0. So if you want the change of choosing between 0.4 and 0.6 in that interval, you can't just sum all chances between 0.4 and 0.6 you'd have infinity x 0 which isn't 0.2 .
Instead, to deal with this 'a lot of really small things' we need a slightly different approach. Then draw a pdf, and talk about area under the curve. Perhaps relate this to the discrete case where the curve is just really blocky.
When we got to continuous distributions, we kind of hit a wall. Here's the puzzle. Suppose the data are recorded to two decimal places, and are reasonably bounded, for instance they are between 0 and 100. That's a discrete distribution. All of the data in the examples and problem sets were fixed-point.
I literally couldn't justify to someone who had never taken calculus, why a wholly different kind of distributions with its own collection of formulas, was necessary or useful. The teacher had never explained it either.