# Uniform distribution

• Sep 7th 2008, 09:31 AM
mtb
Uniform distribution
I just wanted a bit of guidance on the following question.
I will not ask any more questions after this.

Suppose X is a normally distributed random variable, mean M and variance s^2.
Let I(.) denote the distribution function of the standard normal distribution.
Show that U=I((X-M)/s) has a uniform distribution and give the parameters of the distribution.

Thanks
• Sep 7th 2008, 12:58 PM
CaptainBlack
Quote:

Originally Posted by mtb
I just wanted a bit of guidance on the following question.
I will not ask any more questions after this.

Suppose X is a normally distributed random variable, mean M and variance s^2.
Let I(.) denote the distribution function of the standard normal distribution.
Show that U=I((X-M)/s) has a uniform distribution and give the parameters of the distribution.

Thanks

First put $Z=(X-M)/s$

and suppose $a, b \in [0,1],\ b>a$

$p(u \in (a,b))=p(z=I^{-1}(u) \in (I^{-1}(a), I^{-1}(b)))$

................. $=b-a$

RonL