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 $\max$.