Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help needed about Conditional Expectation

  1. Oct 18, 2008 #1
    I need help about conditional expectation for my research. I get stucked on this point. Could anyone show me how to prove that:
    "Let E[|Y|]<∞. By checking that Definition is satisfied, show that if Y is measurable F0, then E[Y|F0]=Y."

    Def: Let Y be a random variable defined on an underlying probability space([tex]\Omega[/tex],F,P) and satisfying E[|Y|]<∞. Let F0 be a sub-[tex]\sigma[/tex]-algebra of F. The conditional expected value of Y given F0,denoted E[Y|F0],is an F0-measurable random variable that also satisfies:E[IFY]=E[IFE[Y|F0]] for all F [tex]\in[/tex] F0

    Note that: Red Fs are sets, but black Fs are sigma-algebras.

    I appreciate any response.
  2. jcsd
  3. Oct 18, 2008 #2
  4. Oct 20, 2008 #3
    Welcome to PF.
    Are you really trying to tell us that is research? To me it sounds like an exercise from a measure theoretic probability course.
    I suggest you show what you have tried so far or look up the answer in a text book.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook