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A gambling machine accepts 5 dollars and generates a random dollar value (x) between 1 and 10.

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A gambling machine accepts 5 dollars and generates a random dollar value (x) between 1 and 10.

  • What is the distribution of x?
  • What is the expected value of x?
  • Is it smart to use this gambling machine?
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The distribution is

  • (1, 1/10), (2, 1/10), (3, 1/10), (4, 1/10), (5, 1/10), (6, 1/10), (7, 1/10), (8, 1/10), (9, 1/10), (10, 1/10)

The expected value is

  • 5.50

It is smart to use this gambling machine as the expected value (5.50) is higher than the cost (5.00).

 

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