I have to construct functions to obtain random numbers from a Gaussian Distribution with mean $\mu$ and variance $\sigma^2$ by using box-muller method and testing the function by sampling from a Gaussian with $\mu=10$ and $\sigma^2=5$. I have to plot the histograms together from a sufficient number of samples with the given distribution function. However, I cannot use NormalDistribution[$\mu$,$\sigma$].
Any ideas on how to do this would be highly appreciated.
For the box-muller method I managed to get this code:
u1 = RandomReal[{0, 1}, 20];
u2 = RandomReal[{0, 1}, 20];
r = Sqrt[-2*Log[u1]];
v = 2*Pi*u2;
x = r*Cos[v]
y = r*Sin[v]