x and z are random variables with distributions - one has n copies of each |
y = S (zi=f(xi))/n is a random variable with a distribution ,even though we only have one value for y we can calculate properties of this distribution including most importantly the expected error in y |
This is most importantly applied in case f(x)=x and the above allows one to calculate error in basic central limit theorem application to y = S xii/n |