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6. [11 marks] A special committee of five professionals is formed from a group of four...

6. [11 marks] A special committee of five professionals is formed from a group of four lawyers, three doctors and three teachers. At least three lawyers are needed in the special committee. Define X as the number of teachers in the special committee.

  1. Construct the probability distribution of the random variable X.
  2. Calculate the expected of X and provide an interpretation of it.
  3. Calculate the standard deviation of X.

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