Variance of a reciprocal uniform

UU is Uniform[0,1][0,1]. Let Y=11+UY = \dfrac{1}{1+U}. What is the variance of YY? (to 3 decimals)

Show hints (2)+
  1. Var(Y) = E[Y^2] - (E[Y])^2; integrate 1/(1+u) and 1/(1+u)^2 over [0,1].
  2. The mean is ln 2 (a log!) and the second moment is 1/2.

Answer

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0.0195 (± 0.001)

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