The body starts beeping , but an explosion in this space could spell disaster for the strike team . <| sep |> 3000 shares of FMCC $ 1 . 82 , 387 of FREJP $ 7 . 87 , and 1800 FNMAS $ 5 . 90 . The numbers in parentheses are the cost basis . I ' m having lots of fun now . <| sep |> from a pure finance perspective , <| sep |> Maybe you guys shouldn ' t have waved nazi flags last time if you want countries like Germany to support you . Eastern Europe neither wants to take in immigrants nor pay for the border . Actually securing the border is an absurdly expensive thing to do and you basically just end up with a situation where you have shoot people . <| sep |> The more general form of the Gaussian density function is fx ~~ mu , sigma f racsigmasqrtmathrmfracxmu 2 sigma . I bring this up because it ' s sort of needed to explain the 12 . We can deduce that for any iid sequence of random variables Xj the variables An 1 n Sumj 1 to n Xj converge almost surely to the mean of X , which I will call mu . Then looking at An mu which goes to zero , we can deduce facts about its rate of convergence . Turns out it converges roughly like 1 sqrtn in the sense that nqAn 0 for q 12 and infty for q 12 . The truly amazing part is that we can actually say what happens at q 12 . This is the CLT . What we can deduce is that the limiting distribution must be of the form C exp D xmu 2 for some constants C and D to be determined . The mu is unavoidable since we are looking at An mu to begin with . Now Intinfty to infty C exp D xmu 2 dx C 1 sqrtD Intinfty to infty expu 2 du C 1 sqrtD sqrt 2 pi . So one constraint on C , D is that C 1 sqrtD sqrtpi 1 since this needs to be a probability distribution . So C sqrtDpi . Now since the Xj are independent , the variances sum . So VarAn 1 n n VarX VarX is constant as we take the limit . Therefore the variance of C exp D xmu 2 must be just sigma 2 the variance of X . Since Intinfty to infty xmu 2 C exp D xmu 2 dx C 1 sqrtD D Intinfty to infty u 2 expu 2 du C sqrtD sqrtpi 2 , this gives the constraint that C sqrtD sqrtpi 2 sigma 2 . As C sqrtDpi , we have that D 12 sigma 2 . So the 12 is really coming from these integrations and our desire to write things in terms of mu and sigma though the idea of considering sigma sqrt 2 rather than sigma makes absolutely no sense probabiitywise , obviously one could avoid the 12 by doing that . In the case when we ' ve normalized to mu 0 and sigma 1 the natural thing to do from a stats point of view , then we get 1 sqrt 2 pi expx 22 as the limiting distribution .