Cumulative distribution function

**losm1** · April 9th 2010, 08:44 AM

This is my first post on MHF, hello everyone.
I need to determine continuous random variable distribution function $f(x)$ based on its cumulative distribution function $<br /> F(x) = \left\{\begin{array}{cc}0&x<0 \\sin(x)&0\leq x \leq \frac{\pi}{2}\\1&x>\frac{\pi}{2}\end{array}\right.<br />$

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

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

Is this correct, and is this formula sufficient?

**qmech** · April 9th 2010, 09:54 AM

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.

**Anonymous1** · April 9th 2010, 11:11 AM

Originally Posted by losm1

$else$

Are you a fluent programmer haha...

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