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**1. The problem statement, all variables and given/known data**

I wrote a code that calculates pi using accept&reject monte carlo integration. It picks -1000000000 pseudo-random points (x,y), and counts the number of points that fall within a unit circle (let's call that number k).

The ratio of k/ N (N = Number of trials = 1000000000) is equal to pi / 4 (the area of the circle / the area of the square around it).

I wish to find the variance so that I may present my result as 3.14158 +- [uncertainty].

**3. The attempt at a solution**

Now, since this is a random (pseudo random really, but anyway) process, the uncertainty should be 1 / sqrt(N). Am I mistaken? Do I have to calculate the variance for both x and y and use error propogation? Thanks in advance.