# cumulative density function

• Mar 20th 2009, 01:28 PM
ben.mahoney@tesco.net
cumulative density function
i have f(x) = (a+1)x^a 0<x<1
I need to find the cumulative density function.
I have had an attempt but im not confident in my answer. It looks too easy!

$\int_0^x (a+1) t^a \, dt$

$= (a+1) \int t^a \, dt$

$= (a+1) \left[ \frac{t^{a+1}}{(a+1)}\right]_0^x$

$= x^{a+1}$.

Does this look correct at all.
Thanks
sorry but i just could not get latex to work
• Mar 20th 2009, 07:30 PM
mr fantastic
Quote:

Originally Posted by ben.mahoney@tesco.net
i have f(x) = (a+1)x^a 0<x<1
I need to find the cumulative density function.
I have had an attempt but im not confident in my answer. It looks too easy!

$\int_0^x (a+1) t^a \, dt$

$= (a+1) \int t^a \, dt$

$= (a+1) \left[ \frac{t^{a+1}}{(a+1)}\right]_0^x$

$= x^{a+1}$, ${\color{red}0 < x < 1}$

Does this look correct at all.
Thanks
sorry but i just could not get latex to work

This looks OK but is incomplete. I'd add the bit in red and also what I have below:

$F(x) = 0$ for $x \leq 0$ and $F(x) = 1$ for $x \geq 1$.