A sample of size \(n=4\) comes from \(\mathrm{Unif}(0,\theta)\) with \(\theta=10\). It is known that \(E[\max X_i]=\tfrac{n}{n+1}\theta\). What is the bias of \(\max X_i\) as an estimator of \(\theta\)?
An estimator \(\hat\theta\) is a rule \(T\), a function of the random sample \(X_i\), that produces a value used to approximate an unknown population parameter \(\theta\).