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Math Help - independent identically distributed R. V's

  1. #1
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    independent identically distributed R. V's

    If {X_i} for i=1,...n are i.i.d, then can we show that {X_i ^2} for i=1,..n are also i.i.d?
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  2. #2
    MHF Contributor matheagle's Avatar
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    yup

    Whatever you had for the distribution of X, your new random variables Y_i=X^2_i

    will all have that new distribution.

    And also if X_i is independent of X_j for i\ne j

    then X_i^2 is independent of X_j^2 for i\ne j
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    iid

    is there a way to show that X_i^2 are independent?
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  4. #4
    MHF Contributor matheagle's Avatar
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    do you want a measure theoretical proof or for just continuous or discrete rvs?
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  5. #5
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    iid

    any one of those is fine. thank you very much
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  6. #6
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    Think about the independence of the sigma-algebras generated by each of the random variable
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