According to Central Limit Theorem, follows a distribution for large n. Also, if 's are iid random variables, then their sum do not follow distribution.
From my understanding, according to the central limit, should behave (roughly) like an N(0,1) distribution for a large enough n.
I'm trying to show this by simulation. I created 1000 iid ~U[0,1]. So according to CLT, T~N(0,1). But how would I show this?
So if I were to plot that, I would get a rouch bell curve, correct? But I try to do this on R
for (i in 1:1000){
+ T=(sum(runif(1000))-(1000/2))/1000*sqrt(1/12*1000)
+ V[i]=T
+ }
I create runif(1000) creates 1000 U[0,1] and T is me trying to standardize it using CLT. I do this 1000 times, but I dont get a bell curve when I plot V.