
Central Limit Theorem
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?

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.

the average of uniforms, when standardized should be approximately normal.
same goes for the sum

so is approximetaly N(0,1)?

since these are iid with a second moment we have
we have

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.

Did you try.......
because yours is wrong, that n in the denominator is incorrect.