Question

You pay $1 to play a game. The game consists of rolling a pair of dice....

You pay $1 to play a game. The game consists of rolling a pair of dice. If you observe a sum of 7 or 11 you receive $4. If not, you receive nothing. Compute the expected value and standard deviation for this game?

Math   Statistics-And-Probability   
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Answer #1

7 or 11 could be obtained here as:

  • 3 + 4 =7
  • 4 + 3 = 7
  • 2 + 5 = 7
  • 5 + 2 = 7
  • 1 + 6 = 7
  • 6 + 1 = 7
  • 6 + 5 = 11
  • 5 + 6 = 11

Therefore there are 8/36 cases where the player wins and receives $4

P(X = 4 - 1 = 3) = 8/36 = 2/9

P(X = -1) = 7/9

Therefore the expected value is computed here as:

The second moment is first computed as:

The standard deviation thus is computed here as:

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