Density function

[kiko]

Dear friends,

 

I kindly ask you to help me show that if X is a normally distributed random variable with parameters mu and sigma squared, then its distribution Phi_x is related to the standard distribution via:

 

 

Phi_X(x)=Phi((x-mu)/sigma)

 

Many thanks!

 

 

 

[mathematic]

Let Y = (X-mu)/sigma. (X and Y random variables).

 

Write down P(Y < y) (standard normal) and then substitute x = mu + y(sigma).