# Math Help - Estimator Unbiased?

1. ## Estimator Unbiased?

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 $\hat{\theta} = Y^2$ unbiased?

The uniform pdf is the function 1/ $\theta$ correct? But then how does this translate to finding the unbiased estimator for $\theta^2$?

2. Obtain the expected value of $Y^2$ and see.

$E(Y^2)= {1\over \theta}\int_0^{\theta}y^2dy={\theta^2\over 3}$

So $3Y^2$ is unbiased for $\theta^2$