Normal RV with mean $1$ and variance $4$ out of standard normal

Question

I have successfully used the Box-Muller algorithm to generate two standard normal random variables. However, my goal is to generate two normal random variables with mean $1$ and variance $4$.

Is there a simple conversion from standard normal to the parameters I've mentioned?

Answer 1

If $Z$ is standard normal then $2Z+1$ does the job.More generally if $Z$ is standard normal, then $\sigma Z+\mu$ is normal, mean $\mu$, variance $\sigma^2$.