A sample of size 1 is drawn from the uniform pdf defined over the interval [0, theta]. Find an unbiased estimator for theta^2. Hint: is theta hat = Y^2 unbiased?

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- Feb 6th 2009, 09:05 PMeigenvector11Unbiasedness
A sample of size 1 is drawn from the uniform pdf defined over the interval [0, theta]. Find an unbiased estimator for theta^2. Hint: is theta hat = Y^2 unbiased?

- Feb 7th 2009, 02:40 AMmr fantastic
Use the hint!

$\displaystyle E(Y^2) = k \theta^2$ therefore $\displaystyle E\left( \frac{Y^2}{k}\right) = \theta^2$ therefore $\displaystyle \frac{Y^2}{k}$ is an unbiased estimator for $\displaystyle \theta^2$.

I leave it to you to get the value of k by solving an appropriate integral.