I'm not totally sure how to even word this question, but I need to find the first and second moments of two variables, $M$ and $N$ as defined by:
$M=\min(X_1,X_2,\dots,X_n)$ and $N=\max(X_1,X_2,\dots,X_n)$ where $(X_1,X_2,\dots,X_n)$ is uniformly distributed on the interval $(0,1)$.
Here's what we have:
I'm a little stuck actually computing the expectations, though. By definition, I know
But I'm getting really confused by the actual computation for my specific purposes of calculating $E[M], E[M^2], E[N], E[N^2]$. Thanks for any guidance.