How can I use the Box-Mueller method to generate generic normal distributions?

Question

Using the box-mueller method, we can generate standar normal distributions from two uniformly distributed random variables.

However, how do we use this method to generate normal distributions with means and variances other than 0 and 1 respectively?

Answer 1

If X is a standard normal random variable (mean $0$ and variance $1$), then $\sigma X+\mu$ is a normal random variable with mean $\mu$ and variance $\sigma^2$. So, just apply this transformation to the samples obtained from the Box-Mueller method.