Chapter 5.4, Problem 8Q

Suppose that 14, 10, 18, and 21 constitute a random sample of size 4 drawn from a uniform pdf defined over the interval $\left[0,\theta \right]$, where $\theta$ is unknown. Find an unbiased estimator for $\theta$ based on $Y_3{}^{\prime }$, the third order statistic. What numerical value does the estimator have for these particular observations? Is it possible that we would know that an estimate for $\theta$ based on $Y_3{}^{\prime }$ was incorrect, even if we had no idea what the true value of $\theta$ might be? Explain.