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Math Help - Finding mean and variance from the mean?

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    Finding mean and variance from the mean?

    Find the mean and variance of the mean of a random sample of 9 from a distribution having pdf 6x(1-x) 0 < x < 1, zero elsewhere.

    I don't even know how to start this one.
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  2. #2
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    Quote Originally Posted by wolverine21 View Post
    Find the mean and variance of the mean of a random sample of 9 from a distribution having pdf 6x(1-x) 0 < x < 1, zero elsewhere.

    I don't even know how to start this one.
    Start with the basic definitions and formulae:


    \bar{X} = \frac{X_1 + X_2 + \, .... \, + X_9}{9}.

    E(\bar{X}) = \frac{1}{9} \left[ E(X_1) + E(X_2) + \, .... \, + E(X_9) \right] = E(X_i)

    where E(X_i) = \int_0^1 6x^2 (1 - x) \, dx.


    Var(\bar{X}) = \frac{1}{81} \left[ Var(X_1) + Var(X_2) + \, .... \, + Var(X_9) \right] = \frac{1}{9} Var(X_i)

    where Var(X_i) = E(X_i^2) - [E(X_i)]^2 and E(X_i^2) = \int_0^1 6x^3 (1 - x) \, dx.
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