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Expected value from a density function

  1. Mar 19, 2008 #1
    I know how to find the expected value from the density function when it is in the form:


    | 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?
  2. jcsd
  3. Mar 19, 2008 #2
    The expectation value of Y is given by

    [tex]E(Y) = \int_{-\infty}^{+\infty}yf(y)dy[/itex]

    If I understood your question correctly, you just have to split the integral into disjoint intervals and apply the different definitions of [itex]f(y)[/itex] in each such interval. This is immediate from the linearity of the Riemann integral and the continuity of the integrand.
  4. Mar 19, 2008 #3
    E(Y) = \int_{-\infty}^{+\infty}yf(y)dy
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