# Normally distributed random variables

• Jun 14th 2008, 04:20 AM
peterpan
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
• Jun 14th 2008, 04:59 AM
mr fantastic
Quote:

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) ......