If a stick of unit length is broken randomly at two points, to make 3 pieces of stick. What is the expected value of the largest stick.

Is there an elegant solution to this problem?



marked as duplicate by JimmyK4542, Graham Kemp, Grigory M, joriki probability Aug 12 '15 at 9:06

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  • $\begingroup$ Try using $2$ uniformly distributed random variables. Then the lengths are given by $X$, $Y-X$ and $1-Y$ (assuming $X<Y$). There might be a simpler model, I'll revisit later. $\endgroup$ – Ennar Aug 12 '15 at 7:08
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    $\begingroup$ Similar question was answered here: math.stackexchange.com/q/14190/99255 $\endgroup$ – srnoren Aug 12 '15 at 7:08