Today I wrote my Statistics, Probability final exam. I feel very confident, and for someone doing very well in that class already, this should not be taken as a sign of arrogance (there are many others, take your pick).
According to my roommate Taylor, he has noticed that I seem to be quite moody today and, to a lesser extent, recently. He asked if it was my time of the month, and I asked whether he would like to settle the matter outside.
From past experience, I only get as described (that would be, dark, moody, etc…) over a very specific subset of things out of the larger set of Life. These would include (mainly):
- while seething over some recent wronging
- during spells of feeling neglected
- when having trouble with girls
Now, let’s say that these three form a mean of sorts, an expected value, with variance being some expression in terms of my relationship status, proximity to other people, and how much duress I am experiencing at the moment of Great Upheavals. Possible values would thusly be varying reasons ranging from predominantly indignation-based (on our graph: left, for some arbitrary reason) to predominantly sadness-based (right).
Now, if each of these Great Upheaval events are distributed with identical underlying distribution models (I’d like to think of it in terms of some exponential distribution, where we consider only the wait time before the first event), then the Central Limit Theorem suggests that given enough observed Upheavals, the distribution of them all as a whole could be approximated by, you guessed it, the Normal Distribution.
This makes a lot of sense, since most everything in Nature tends towards some Normal Distribution model, be it the weight of individual penguins or termites per mound. Some say this is a quantifiable argument for God’s existence, but this more rationally explained by the underlying mathematics present. However, the elegance and perfection with which the underlying mathematics works out—now that is more like an argument for God’s designing hand in my somewhat educated opinion.
Also, the integral of e^(-x^2) from zero to infinity (mostly un-integrable by non-math nerds) works out to be the square root of Pi divided by 2 (i.e. √π/2) and this is where the Normal Distribution’s Probability Density Function is derived. Yeah, I know. Calculus, meet Statistics.
I am also not feeling so great. Physically, very healthy. Otherwise, not in the best shape, as I came to realize today. I should probably seek medical attention wherever and as soon as possible.
