# Thread: Normally distributed random variables

1. ## Normally distributed random variables

Im finding it hard to understand why you can do the following transformation of $\displaystyle \phi$ to get from a normally distributed random variable with mean 0 and standard deviation of 1 to a normally distributed random variable with a specific mean and standard deviation:

mean + standard deviation $\displaystyle \cdot \phi$

Finding it difficult to see the intuition behind multiplying by std. dev. and adding the mean.

This is a pretty fundamental thing to understand so would be grateful for any help.

Cheers,
Peter

2. Originally Posted by peterpan
Im finding it hard to understand why you can do the following transformation of $\displaystyle \phi$ to get from a normally distributed random variable with mean 0 and standard deviation of 1 to a normally distributed random variable with a specific mean and standard deviation:

mean + standard deviation $\displaystyle \cdot \phi$

Finding it difficult to see the intuition behind multiplying by std. dev. and adding the mean.

This is a pretty fundamental thing to understand so would be grateful for any help.

Cheers,
Peter
All you're doing is translating and dilating (scale changing) ......