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Monte-Carlo Integration and
Monte-Carlo Integration and the Central Limit Theorem---II
Let
where
are distributed according to
.
Now apply central limit theorem to
.
are independent identically distributed random variables with
mean
and
variance
.
Then according to the Central Limit Theorem
or
I
can be estimated as
with error
.
Geoffrey Fox
,
Northeast Parallel Architectures Center
at Syracuse University,
gcf@npac.syr.edu
where 
are distributed according to 
.
.
are independent identically distributed random variables with
mean 
and
variance 
.
with error 
.