The central-limit-theorem tag has no wiki summary.
6
votes
1answer
233 views
Limiting distribution of a squared sum of random variables
Let $S_n = \frac{1}{n}\sum_{i=1}^n X_i$, and $T_n = \frac{1}{n}\sum_{j=1}^nY_i$, where
The $X_i$ are iid, the $Y_i$ are iid (with a different law)
$X_i$, and $Y_i$ are dependent
For $i\neq j$, ...
10
votes
3answers
646 views
What is the sum of squared t variates?
Let $t_i$ be drawn i.i.d from a Student t distribution with $n$ degrees of freedom, for moderately sized $n$ (say less than 100). Define
$$T = \sum_{1\le i \le k} t_i^2$$
Is $T$ distributed nearly as ...
2
votes
1answer
249 views
Central Limit Theorem Tails
I'm trying to compute some p-values for samples from a distribution of sums of ~1000 random variables. The exact distribution of these random variables isn't known, but I have empirical estimates that ...
13
votes
2answers
384 views
How to know which probability distribution to expect?
Currently I am analyzing social networks (not virtual) and I am observing the connections between people. If a person would choose another person to connect with randomly, the number of connections ...
28
votes
5answers
2k views
What intuitive explanation is there for the central limit theorem?
In several different contexts we invoke the central limit theorem to justify whatever statistical method we want to adopt (e.g., approximate the binomial distribution by a normal distribution). I ...
3
votes
4answers
640 views
Difference between Excel's RAND(), RAND()*RAND(), etc
I plotted below the standarized results of:
RAND()
RAND() * RAND()
...
RAND() * RAND() * RAND() * RAND() * RAND() * RAND()
It seems that the results are getting to zero, is that because you're ...
16
votes
5answers
737 views
Test for finite variance?
Is it possible to test for finiteness (or existence) of the variance of a random variable given a sample? As a null, either {the variance exists and is finite} or {the variance does not exist/is ...
20
votes
7answers
1k views
How do you convey the beauty of the Central Limit Theorem to a non-statistician?
My father is a math enthusiast, but not interested in statistics much. It would be neat to try to illustrate some of the wonderful bits of statistics, and the CLT is a prime candidate. How would you ...
