# Cumulative distribution function

• Apr 9th 2010, 08:44 AM
losm1
Cumulative distribution function
This is my first post on MHF, hello everyone.
I need to determine continuous random variable distribution function $\displaystyle f(x)$ based on its cumulative distribution function $\displaystyle F(x) = \left\{\begin{array}{cc}0&x<0 \\sin(x)&0\leq x \leq \frac{\pi}{2}\\1&x>\frac{\pi}{2}\end{array}\right.$

Having $\displaystyle F'(x)=f(x)$ (fundamental theorem of calculus) I would say that distribution function should look like this:

$\displaystyle f(x) = \left\{\begin{array}{cc}cos(x)&0\leq x \leq \frac{\pi}{2}\\0&else\end{array}\right.$

Is this correct, and is this formula sufficient?
• Apr 9th 2010, 09:54 AM
qmech
Yes that's right. It's also sufficient, although you might make it clearer that your function is 0 everywhere other than the interval 0 to pi/2.
• Apr 9th 2010, 11:11 AM
Anonymous1
Quote:

Originally Posted by losm1
$\displaystyle else$

Are you a fluent programmer haha... (Wink)