Finding expectation of peicewise mixed distribution density function

[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) ?

 

[HallsofIvy]

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

 

[torquerotates]

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

 

[chiro]

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) ?

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.