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Math Help - Expected values and Variances

  1. #1
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    Expected values and Variances

    Question 1:
    Let where Xi's be i.i.d. Normal with mean 10 and variance 4 for i=1,2,...,16 and Yj's be i.i.d. Normal with mean 15 and variance 12 for j=1,2,...,10 and Ix & Yj are independent for all i & j. What is the value of E[W] and Var(W)?


    Question 2:
    Let Y= where Xi's be i.i.d. Normal with mean 10 and variance 4 for i=1,2,...,32. What is the value of E[Y] and Var(Y)?


    Two very similar problems, but I'm lost. The rest of the homework is spelled out very carefully with hints, and these two are just on their own. I don't even know where to begin.
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  2. #2
    Moo
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    Hello,

    First look here : Chi-square distribution - Wikipedia, the free encyclopedia
    Your normal rv's are all subtracted by their mean, so X_i-10 and Y_i-15 are actually normal distributions with mean 0.
    In order to make them standard normal distributions, recall that \frac{X_i-\mu}{\sigma} follows a N(0,1).

    Then look here : F-distribution - Wikipedia, the free encyclopedia

    which will give you the results you're looking for.
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  3. #3
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    Thanks. That is just what I needed.
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