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A machine produces $0$, $1$ or $2$ defective pieces in a day with associated probability of $1/6$, $2/3$ and $1/6$, respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are

  1. $1$ and $1/3$
  2. $1/3$ and $1$
  3. $1$ and $4/3$
  4. $1/3$ and $4/3$
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