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Expectation of X^Y

  1. Dec 11, 2003 #1
    Can anyone let me know the estimator for the expectaiion of X^Y. X and Y are iid random variables, and their expectation are E(X) and E(Y) respectively.

    Thank you.
     
  2. jcsd
  3. Dec 11, 2003 #2

    Hurkyl

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    I'm pretty sure that's not enough information.
     
  4. Dec 11, 2003 #3
    Okay, let me put this way. Let E(X) be the expectation of random variable X, and X and Y are independent and identically distributed random variables. My question is, what is E(X^Y)? I did Talyor expansion of X^Y and concluded that, for small variances for X and Y, E(X^Y)=E(X)^E(Y).

    Is this correct?
    Thank you for your help in advance.
     
  5. Dec 11, 2003 #4

    Hurkyl

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    It's (probably) true that if the distributions of X and Y are "close" to constant, then then E(X^Y)=E(X)^E(Y) is approximately true.

    My gut says that small variances isn't enough, but I haven't done the calculations to be sure.
     
  6. Dec 11, 2003 #5

    mathman

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    I believe it is not true. Try a simple particular case. For example assume X and Y are uniformly distributed over some interval, and work out E(XY).
    A good crazy example would use two intervals symmetrical around 0 (avoid 0 itself), then E(X)E(Y) would be 00, which would be nonsense.
     
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