An easy example to show that there is no "magic N" for the Central
Limit Theorem is the Poisson distribution with very small lambda. If X
and Y are Poisson lambda and Poisson mu respectively, their sum is
Poisson (lambda+mu). So, for instance, if X is Poisson (1/3000), the sum
of 300 such independent variables is Poisson (1/10), still very far from
normal; and this X has a distribution to which the CLT eventually does
apply.
Then of course there's the Cauchy distribution which _never_ settles
down...
-Robert Dawson
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