 # Reading 10 Example 3-> variance

Hi, Why is the variance of capital expenditures is (100-0)^2 / 12? Where is the 12 coming from? Thanks.

Seems to be a given formula with some heavy “difference equations” math behind it. It is referenced in reading 9, example 7 as well, and just given (p. 388). Best reference I have found to it in a few minutes of digging is in paragraph 4 of the following page. http://www.mathreference.com/pr,unif.html Hopefully the coming pages in the reading will enlighten us both.

elighcash Wrote: ------------------------------------------------------- > Seems to be a given formula with some heavy > “difference equations” math behind it. It is > referenced in reading 9, example 7 as well, and > just given (p. 388). > Best reference I have found to it in a few minutes > of digging is in paragraph 4 of the following > page. > > http://www.mathreference.com/pr,unif.html > > Hopefully the coming pages in the reading will > enlighten us both. Is this the variance of a uniform distribution (as suggested by that reference)? If so, it’s a very simple integral. Difference equations are discrete versions of differential equations. In general, difference equations are harder to solve (that discrete things are almost always harder to solve than continuous things is something that still blows my mind when I get in touch with it). You can use difference equations for finding out interesting things about stochastic processes but applications in statistics/data analysis are pretty rare.

Since I’m sitting here thinking about it - Somehow the whole universe is discrete - everything seems to be quantized and even space seems divided into distances longer than the Planck length (i.e., in some sense it seems to be nonsensical to say that two things are 10^-40 meters apart). But mathematics works in exactly the opposite way - discretizing things almost always makes them harder. For example, a stock price is really a finite state thing and for most derivatives we care only about settlement prices that happen at discrete times. That means we should do derivatives pricing with this simple structure and use Markov chains to price derivatives. Except that it is a serious pain and nowhere near as powerful as imposing this geometric Brownian motion thing on it and using stochastic calculus (which isn’t nearly as difficult as is frequently supposed). It’s like God gave us the tools to understand some other universe, not the one we happen to live in. Jerk.

I knew this was beyond me. I am just going to take this as given, if it ever even comes up again in the readings. Wikipedia articles for continuous distributions and variance also do not seem to explain it. It is there also just a given on the right hand column of the relevant wiki articles. Bump.

yes, I couldn’t find the answer on wiki either. I thought it might have something that was supposed to be “intuitive” like the mean calculation. I guess not.

IS this just hte variance of a uniform? Just take integral of (1/(b-a))^2 from a to b - ((b+a)/2)^2 and simplify. It’s just the defn of variance and an integral so simple it is the area of a rectangle.