[stuff about the CLT deleted]
So you can use R usefully to eveluate general statisical issues of this kind!
absolutely! R is excellent for this sort of thing. I use it for teaching stats all the time.
I'd say that without a tool like R you cannot learn statistics.
Consider an exponential distribution, which is very skewed.
f <- function(n){mean(rexp(n))}then f(10) gives the mean of 10 independent exponentially distributed random
variables. Then
hist(replicate(10000,f(10)))
gives us a histogram of 10000 observations of a variable that is itself the mean of 10 exponential variables. It still looks a bit skew to me. Try 100 exponential variables:
hist(replicate(10000,f(100)))
Still a tiny bit skew.
hist(replicate(1000,f(1000))) which is indistinguishable from a Gaussian.
So as n -> infinity, the CLT kicks in. But here 100 is a bit less than infinity and 1000 ~= infinity.
It's one thing to know a theoretical result, it's quite another to verify it numerically.
Kia Ora
Best wishes, Ted.
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