# cumulative density function

• Mar 20th 2009, 12:28 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!

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

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

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

$\displaystyle = x^{a+1}$.

Does this look correct at all.
Thanks
sorry but i just could not get latex to work
• Mar 20th 2009, 06:30 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!

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

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

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

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

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:

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