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TIFR ECE 2019 | Question: 6

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Suppose that $X_{1}$ and $X_{2}$ denote the random outcomes of independent rolls of two dice. Each of the dice takes each of the six values $1,2,3,4,5$, and $6$ with equal probability. What is the value of the conditional expectation

\[\mathbf{E}\left[\max \left(X_{1}, X_{2}\right) \mid \min \left(X_{1}, X_{2}\right)=3\right] ?\]

  1. $33 / 7$
  2. $4$
  3. $5$
  4. $9 / 2$
  5. $19 / 4$

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