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The Central Limit Theorem
:
the sum of a
large
number of identical, independent
random variables is approximately
normally
distributed.
So, if I want to calculate an unknown quantity, m,
and k is a random variable of expectation value E(k)=m and variance Var(k)=b
2
.
If k
1
, k
2
, …, k
N
are N RANDOMLY selected values of k,
then:
is normally distributed with E( )=Nm and V ( )=Nb
2
or equivalently:
or:
So, if I want to estimate the photon fluence (or any related quantity ) at point r, I
can average the contribution of N photon tracks RANDOMLY sampled from the
probability distribution of all possible tracks
The MC method …