# Unbiasedness

• February 6th 2009, 09:05 PM
eigenvector11
Unbiasedness
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?
• February 7th 2009, 02:40 AM
mr fantastic
Quote:

Originally Posted by eigenvector11
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?

Use the hint!

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

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