# Sample normal distribution given standard normal samples

I have a method which returns random samples from a standard normal distribution, i.e. mean 0 and standard deviation 1.

How can I alter these samples so they have a different deviation? For example, I want to sample from a normal distribution with mean 0 and standard deviation 2?

What operation do I need to apply to the samples from the standard normal distribution?

• If $U\sim \text{Norm}(0,1)$ then $\sigma U+\mu\sim \text{Norm}(\mu,\sigma^2)$. Is that what you mean to ask for special case $\mu=0$ and $\sigma=2$? – drhab Oct 31 '16 at 11:53
• @drhab This is exactly what I meant. Thanks – JNevens Oct 31 '16 at 11:54