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Consider two independent random variables $\left(U_{1}, U_{2}\right)$ both are uniformly distributed between $[0,1]$. The conditional expectation

\[E\left[\left(U_{1}+U_{2}\right) \mid \max \left(U_{1}, U_{2}\right) \geq 0.5\right]\]

equals

  1. $7 / 6$
  2. $8 / 7$
  3. $6 / 7$
  4. $1.1$
  5. None of the above

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