If the variables $\alpha_1$...$\alpha_n$ are distributed uniformly in $(0,1)$,
- How do I show that the spread $\alpha_{(n)}$ - $\alpha_{(1)}$ has density $n (n-1) x^{n-2} (1-x)$ and expectation $(n-1)/(n+1)$?
- What is the probability that all $n$ points lie within an interval of length $t$?