I have been following the online MIT statistics course, and one course was about some fundamental distributions.(https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/readings/MIT18_05S14_Reading5c.pdf)
I read it a couple of times and did a lot of search online, but I still find it hard to fully grasp the idea of how to match different distributions to different real life scenarios.
For example, "Suppose we have a tape measure with markings at each millimeter. If we measure (to the nearest marking) the length of items that are roughly a meter long, the rounding error will uniformly distributed between -0.5 and 0.5 millimeters." I just cannot wrap my head around how it was determined that uniform distribution matches this case.
I'm wondering if there are some books/articles that give detailed and intuitive explanation of distributions and their real life applications?
Thanks!
I haven't used this myself, but I browsed it now and it seems very good. Though I'd want some more real life stuff there - I'll add to this if I find any.
(second day that the original link doesn't work, so I substitute yet another)
http://www.fysik.su.se/~walck/suf9601.pdf
As for your particular distribution: There are many slices of measurements, so it is practically random where the result lies around a certain millimeter mark. If you had a measure with 10 cm scale, then the depiction "roughly a meter long" would already work to make it somewhat skewed.
Quite obvious, but I add this anyway: with that 10 cm spaced measure, you would get the same distribution again if the results were roughly 100 meters long.