November 18th, 2008, 04:56 AM
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 | Flow Master | | Join Date: Dec 2007 Location: Zeitgeist
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Quote:
Originally Posted by wolverine21  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:  . ![E(\bar{X}) = \frac{1}{9} \left[ E(X_1) + E(X_2) + \, .... \, + E(X_9) \right] = E(X_i)](http://www.mathhelpforum.com/math-help/latex2/img/1cb08ebf883be536734e7c8a3e93ef39-1.gif "E(\bar{X}) = \frac{1}{9} \left[ E(X_1) + E(X_2) + \, .... \, + E(X_9) \right] = E(X_i)")
where  . ![Var(\bar{X}) = \frac{1}{81} \left[ Var(X_1) + Var(X_2) + \, .... \, + Var(X_9) \right] = \frac{1}{9} Var(X_i)](http://www.mathhelpforum.com/math-help/latex2/img/46cb02b1a71f37b1417c5d5b7e29facc-1.gif "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](http://www.mathhelpforum.com/math-help/latex2/img/f26092801bde6e7adf74655e9840a187-1.gif "Var(X_i) = E(X_i^2) - [E(X_i)]^2") and  .
__________________ There are two things you should never try to prove: the impossible and the obvious. The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)
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