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Math Help - expectation

  1. #1
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    expectation

    suppose you have a sequence of random variables (X_n)_{n \geq 0}. Then what does sup_n E[X_n] mean? it does not make sense to me since if n is fixed then E[X_n] is a constant. Is it the same thing as lim sup_{n-> \infty} E[X_n]?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Kat-M View Post
    suppose you have a sequence of random variables (X_n)_{n \geq 0}. Then what does sup_n E[X_n] mean? it does not make sense to me since if n is fixed then E[X_n] is a constant. Is it the same thing as lim sup_{n-> \infty} E[X_n]?

    E[X_n] is a constant
    So all you're asking is what is a supremum of a sequence a_n
    limsup is the limit of the largest subsequence.
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  3. #3
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    expectation

    so sup_n E[X_n]=sup_{j \leq n }E[X_j]?
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