$X_1$ , a sample size 1 is drawn from a uniform distribution over $[0,\theta]$. Find an unbiased estimator for the variance of the population. Find a function for $X_1$, $\tau(X_1)$ such that $E(\tau(X_1))=\theta^2/12$.
I know the expected value of this uniform distribution can be found $$\int_{0}^{\theta} x(\frac{1}{\theta}) dx$$. Would I just be looking for some x such that $$\int_{0}^{\theta} x(\frac{1}{\theta}) dx=E(\tau(X_1))=\theta^2/12$$
[self-study]
tag & read its wiki. $\endgroup$