Finding expectation of peicewise mixed distribution density function

1. Mar 22, 2012

torquerotates

If I am given the CDF of a piecewise mixed distribution density starting from a and ending at b, would the expected value just be a + integral(all the pieces) ?

2. Mar 22, 2012

HallsofIvy

Staff Emeritus
If there were only one "piece" would the expected value be a+ the integral of that piece?

3. Mar 22, 2012

torquerotates

I suppose not. It would just be the integral of that piece. But if it were two or more?

4. Mar 23, 2012

chiro

Hey torquerotates.

Why don't you just differentiate each piece of your CDF and then use the definition of expectation?

If you function is in discrete form or a form that is non-integrable (non-Riemannian) then you can either just look at the deltas if you have a discrete distribution for that piece, or if its in a Lebesgue form just use the properties of the characteristic function to get your PDf for that piece.