# Thread: mean value from a CDF

1. ## mean value from a CDF

Hi, I'm not sure if this post is in the right place, but it's a university level question anyhow...

Random variable X has a cumulative distribution function (CDF) given by:
$F_{X}(x) = \left\{\begin{matrix}0\; \; \; \; x\leqslant 0\\ x/2\; \; \; \; x\,\epsilon \: (0,2)\\1\; \; \; \; x\geq2\end{matrix}\right.$

What is its mean value?

I'd seriously appreciate some help on this one - I'm not statistically minded at all and I'm finding the whole pdf cdf thing really confusing.

Rorosingsong

2. ## Re: mean value from a CDF

this is a uniform (0,2)
Hence the mean is 1

3. ## Re: mean value from a CDF

Hi matheagle!

Thanks for your prompt reply, but I'm new to stats and not sure of what you mean by a "a uniform (0,2)"...

Could someone explain the working to me? I know it involves integrating FX(x), but I don't understand why x smaller than or equal to 0 or x larger than or equal to 2 aren't involved...

Thanks,
rorosingsong

4. ## Re: mean value from a CDF

Originally Posted by rorosingsong
Hi matheagle!

Thanks for your prompt reply, but I'm new to stats and not sure of what you mean by a "a uniform (0,2)"...

Could someone explain the working to me? I know it involves integrating FX(x), but I don't understand why x smaller than or equal to 0 or x larger than or equal to 2 aren't involved...

Thanks,
rorosingsong
The pdf is given by dF/dx, from which what is said in post #2 should be obvious. If it's not obvious, then use the the pdf and the definition of mean to do the calculation directly.

5. ## Re: mean value from a CDF

Your book should have the uniform density in it.
It's the most basic continuous density.