Expected value and nonnegative random variable

  1. Hi All,

    i got a short question concerning the ev of a monotone decreasing function.

    when i got a nonnegative random variable t, then its ev (with a continuous density h(.)) is given by
    Then if v is a nonpositive random variable, is its ev given by
    i got that the ev of a monotone increasing function g(x) is:

    Now, let b(x) denote a monotone decreasing function. Therefore: z(x)=-b(x) is a monotone increasing function.
    Am I correct, that it got the ev of b(x) by
    and thus
    E(b(x))= - [int]z'(x)(1-F(x))dx

    any thoughts are highly appreciated!

    thanks alot!
  2. jcsd
  3. EnumaElish

    EnumaElish 2,332
    Science Advisor
    Homework Helper

Know someone interested in this topic? Share this thead via email, Google+, Twitter, or Facebook

Have something to add?