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Expectation and Variance

  1. Feb 10, 2008 #1
    1. The problem statement, all variables and given/known data

    Say X has a density f(x) = 3x^(-4) if x > 1, and 0 otherwise. Now say X1,...,X16 are independent with density f. Let Y = (X1X2...X16)^(1/16). Find E(Y) and Var(Y).

    2. Relevant equations

    Var(Z) = E(Z^2) - [E(Z)]^2
    E(Z) = Integral from -inf to +inf of z*f(z)dz

    3. The attempt at a solution

    I found E(X) = 3/2 and Var(X) = 3/4, using the above formulas. However, I still do not even know how to approach the actual question of the problem.

    Thank you all in advance!
     
  2. jcsd
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