# cumulative distribution function problem

• Aug 4th 2012, 09:24 PM
bryce09
cumulative distribution function problem
I have this question I am trying to get through but i keep coming into trouble. The question is:

Show that the cumulative distribution function from a uniform distribution of the random variable is Fx(y) = (y-a) / (b-a) for some a < y < b

I've started the question but have become stuck going from here

y
∫ x/(b-a) dx
a

when i integrate i come up with y2-a2/2(b-a). When i'm pretty sure it should come out as (y/b-a)-(a/b-a) which would then solve to y-a/b-a

any advice as to what i'm forgetting to do would help me alot, thanks.
• Aug 5th 2012, 02:56 AM
Plato
Re: cumulative distribution function problem
Quote:

Originally Posted by bryce09
Show that the cumulative distribution function from a uniform distribution of the random variable is Fx(y) = (y-a) / (b-a) for some a < y < b
I've started the question but have become stuck going from here
y
∫ x/(b-a) dx

You want to start with $\displaystyle \int_a^y {\frac{{dx}}{{b - a}}}~.$
• Aug 5th 2012, 03:26 AM
bryce09
Re: cumulative distribution function problem
Ok that makes sense, so the dx just integrates to x doesn't it. which then goes into y-a/1.
Silly question, but why is it that there is no x, and just dx?