Suppuse X is uniformly distributed on ( 0, theta). suppose we estimate theta with the maximum value from a random sample of size n. Compute the mean squared error for the estimator.
You need the density of the largest order stat from a $\displaystyle U(0,\theta)$.
The orginal density is $\displaystyle {1\over \theta}$ on $\displaystyle (0,\theta)$.
F(x) is $\displaystyle {x\over \theta}$ on $\displaystyle (0,\theta)$.
And the density of $\displaystyle F_{(n)}(x)=n(F(x))^{n-1}f(x)$ on $\displaystyle (0,\theta)$.
From that you can answer all your questions.