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Conditional expectation

  1. Aug 17, 2006 #1
    Is it possible to solve for E(Y) and var (Y) when I am only given the distribution f(Y|X)?

    I can solve for E(Y|X). But is it possible to find E(Y) and var(Y) given only this info?
  2. jcsd
  3. Aug 17, 2006 #2


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    No it is not. Let Y be distributed as f(x) = .5 if x = -1 or 1, 0 otherwise. Let X be distributed as f(x) = 1 if x = 1, 0 otherwise. Then f(Y|X) is the distribution of X. You can change the mean and variance of Y to almost whatever you want by moving the other probability mass, and f(Y|X) will not be affected.
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