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?

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!

therefore therefore is an unbiased estimator for .

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