Variance of the longer piece

MediumProbability Random Variables~5m

A $1$ -metre rope is cut at a single uniformly random point, giving two pieces. Let $L$ be the length of the longer piece. Compute $\operatorname{Var}(L)$ .

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$L=\max(U,1-U)$ lives in $[\tfrac12,1]$ . Find its CDF there.
It's $\text{Uniform}(\tfrac12,1)$ ; variance of a length- $\tfrac12$ uniform is $(1/2)^2/12$ .

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0.0208 (± 0.001)

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Variance of the longer piece

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