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Math Help - Doubt: Expected Values of Bivariate Random Variables

  1. #1
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    Doubt: Expected Values of Bivariate Random Variables

    E[X|Y, Z] = E[X|Y]

    I am given a problem with this condition. Please tell me what the left hand side term mean?? and what can we write for it??
    E[X|Y, Z] = ??
    (I expect something in terms of Joint PDF or Conditional PDF.If that cannot be done, please tell me any other way)
    I know what to write for E[X|Y]. But what should we write for E[X|Y, Z]?? URGENT!! (Tell me if my question is not clear!!)
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  2. #2
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    Quote Originally Posted by devd View Post
    E[X|Y, Z] = E[X|Y]

    I am given a problem with this condition. Please tell me what the left hand side term mean?? and what can we write for it??
    E[X|Y, Z] = ??
    (I expect something in terms of Joint PDF or Conditional PDF.If that cannot be done, please tell me any other way)
    I know what to write for E[X|Y]. But what should we write for E[X|Y, Z]?? URGENT!! (Tell me if my question is not clear!!)
    Hi there. I think (could be wrong after all) that it's something like:

    \mathbb{E}(X|(Y,Z)),

    that is, you treat Y,Z as a random vector. I don't know if this helps but you can condition a variable with respect to any random variable, also vectors.
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  3. #3
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    Quote Originally Posted by devd View Post
    E[X|Y, Z] = E[X|Y]

    I am given a problem with this condition. Please tell me what the left hand side term mean?? and what can we write for it??
    E[X|Y, Z] = ??
    (I expect something in terms of Joint PDF or Conditional PDF.If that cannot be done, please tell me any other way)
    I know what to write for E[X|Y]. But what should we write for E[X|Y, Z]?? URGENT!! (Tell me if my question is not clear!!)[/QUOTE]
    E[X|Y,Z] means the expected value of X, given specific values of Y and Z. Saying that is equal to E[X|Y], the expected value of x given a specific value of Z, tells you that X is independent of Z.
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