# Thread: Uniform distribution

1. ## 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

2. 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 $\displaystyle Z=(X-M)/s$

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

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

................. $\displaystyle =b-a$

RonL