Suppose that $X\_1,\cdots, X\_n$ are independent random variables from uniform distribution on interval $(\theta\_1,\theta\_2)$, $\theta\_2>\theta\_1>0$. It is know that $T(X)=(X\_{(1)},X\_{(n)})$ is the complete sufficient statistic for $(\theta\_1,\theta\_2)$.

Find the expectations of the largest and smallest order statistics $X\_{(n)}$ and $X\_{(1)}$ respectively.

Hint: Use the transformation $Y=\frac{X-\theta\_1}{\theta\_2-\theta\_1}$

How do I use the hint to solve the problem?