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Question regarding variance and independence

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  • Question regarding variance and independence

    I'm studying for exam P/1 and have encountered many questions, but this is one of the newest problems I am struggling to understand. I figured this forum would be a good place to start for questions explaining the concepts behind some of these questions.

    The problem I encountered is regarding independence of randomly selected variables. The solution in the P/1 Study Manual states that...

    "T= X1+Y1+X2+Y2+...+X100+Y100 = T1+T2+...+T100.
    X and Y are independent of one another and Ti's are independent of one another."

    Then in the solution of Var(Ti) the Cov(X,Y) is included. I'm unsure why this is. I thought that covariance was not included in independent calculations of variance.

    Any help regarding this question is greatly appreciated.

    Thanks

  • #2
    Re:

    My best guess is that this is a trick question, because with the information given the only way to solve the problem is by using the Cov(X,Y) in the Var calculation.

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