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Consider a random variable $X$ that takes integer values $1$ through $10$ each with equal probability. Now consider random variable
\[
Y=\min (7, \max (X, 4)).
\]
What is the variance of $Y?$ 

  1. $121 / 4$
  2. $37 / 20 $
  3. $9 / 5$
  4. $99 / 12$
  5. None of the above
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