Expected value from a density function

[mind0nmath]

Hey,
I know how to find the expected value from the density function when it is in the form:

(example)

| y^2 -1<y<1
|
fy =|
| 0 elsewhere

Ey = integral(upper limit 1, lower limit -1)[y*y^2 dy)

but, what if the density function looks like this:

| y^2 -1<y<0
|
fy =| y^2 - y 0<y<1
|
| 0 elsewhere

how do you approach here?

 

[maverick280857]

The expectation value of Y is given by

E(Y) = \int_{-\infty}^{+\infty}yf(y)dy[/itex]<br /> <br /> If I understood your question correctly, you just have to split the integral into disjoint intervals and apply the different definitions of f(y) in each such interval. This is immediate from the linearity of the Riemann integral and the continuity of the integrand.

 

[tomyus]

E(Y) = \int_{-\infty}^{+\infty}yf(y)dy