# Normal distribution

1. Jun 4, 2012

### Kinetica

Show that if X is a normally distributed random variable with parameters mu and σ2, then then show that for each real number x we have:

фX(x)=ф[(x-m)/σ]

I have really hard time. Any possible hint is greatly appreciated.

Last edited: Jun 4, 2012
2. Jun 4, 2012

### micromass

Staff Emeritus
What is the definition of ф[(x-m)/σ], write out the left hand side and the right hand side.

3. Jun 5, 2012

### Kinetica

I know that

Z= [X-μ]/σ or X=σ Z+μ

I also know that

f(x,μ,σ2)=1/ √(2πσ) e -(x-μ)2/(2σ2)=1/σ ф((x-μ)/σ)