We have a roulette with the circumference $a$. We spin the roulette 10 times and we measure 10 distances, $x\_1,\ldots,x\_{10}$, from a predefined zero-point. We can assume that those distances are $U(0,a)$ distributed.

An estimation of the circumference $a$ is given:

$$a^\* = \max(x\_1,\ldots,x\_{10})$$

To check whether it's biased or not I need to calculate:

$$E(a^\*) = E(\max(x\_1,\ldots,x\_{10}))$$

How do I proceed? I don't know any rules for calculating the estimate of a $\max$.