Suppose that a point is chosen at random on a stick that has length 15 inches, and that the stick is broken into two pieces at that point. Find the expected value of the lengths of the two pieces.
Can anyone help me set this one up???
does random mean uniform?
if so then, let $\displaystyle X\sim U(0,15)$ be where we cut this stick.
so the lengths are X and 15-X.
Since $\displaystyle E(X)=15/2$ we have
$\displaystyle E(X)=15/2 $ and $\displaystyle E(15-X)=15-E(X)=15-15/2=15/2 $ as the two expected lengths.