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Math Help - i.i.d random variables

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    i.i.d random variables

    Suppose W, X, Y and Z are i.i.d random variables with mean "mu" = -9 and standard deviation "sigma" = 6

    Find the expectation and variance of each of the following estimators of "mu"

    1. A = 8W + 3X - 4Y - 6Z

    i got E(A) = -9 and Var(A) as 3976.... however i am having problems knowing whether i was right to convert the SD of 6 to a variance of 36?

    2. B = 1/28(8W + 6X +2Y +9Z)

    3. C = 33W + 4Y - 36Z

    Which estimators are unbiased for "mu"?

    Which estimator is the most efficient?

    Find E(YW)
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    Quote Originally Posted by sirellwood View Post
    Suppose W, X, Y and Z are i.i.d random variables with mean "mu" = -9 and standard deviation "sigma" = 6

    Find the expectation and variance of each of the following estimators of "mu"

    1. A = 8W + 3X - 4Y - 6Z

    i got E(A) = -9 and Var(A) as 3976.... however i am having problems knowing whether i was right to convert the SD of 6 to a variance of 36? Mr F says: You were right. Do the others the same way.

    2. B = 1/28(8W + 6X +2Y +9Z)

    3. C = 33W + 4Y - 36Z

    Which estimators are unbiased for "mu"? Mr F says: Which estimators have an expected value equal to mu ....?

    Which estimator is the most efficient? Mr F says: What does the definition of efficient tell you ....?

    Find E(YW)
    E(YW) = \int_{- \infty}^{+ \infty} \int_{- \infty}^{+ \infty} yw f(y, w) \, dw \, dy where f(y, w) = f(y) f(w) is the joint pdf of Y and W ....
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